diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index b0b5ee00..d41468bd 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -41,6 +41,7 @@ jobs:
           python3 scripts/audit_floor_excursion.py
           python3 scripts/audit_five_band_clock.py
           python3 scripts/audit_rational_band_obstruction.py
+          python3 scripts/audit_wider_band_clock.py
 
       - name: Check exact first-descent intervals
         run: |
diff --git a/Collatz.lean b/Collatz.lean
index 6b6f7210..793a996d 100644
--- a/Collatz.lean
+++ b/Collatz.lean
@@ -2111,3 +2111,4 @@ import Collatz.Exploration.TwoStepCapacity
 import Collatz.Exploration.FloorExcursion
 import Collatz.Exploration.FiveBandClock
 import Collatz.Exploration.RationalBandObstruction
+import Collatz.Exploration.WiderBandClock
diff --git a/Collatz/Exploration/BandClock.lean b/Collatz/Exploration/BandClock.lean
new file mode 100644
index 00000000..ad238635
--- /dev/null
+++ b/Collatz/Exploration/BandClock.lean
@@ -0,0 +1,79 @@
+import Collatz.Exploration.BarrierKernel
+
+/-! Consequences of a proved fixed-barrier exit clock. The abstraction preserves
+both exit directions and gives finite-prefix witness counts at rational thresholds. -/
+namespace Collatz.Exploration.BandClock
+open BarrierKernel
+
+def ExitClock (P Q K : Nat) : Prop :=
+  ∀ b n : Nat, 1 < b → ∃ k, k ≤ K ∧ (orbit k n < b ∨ P*b < Q*orbit k n)
+
+theorem no_band_through {P Q K b n : Nat} (hc : ExitClock P Q K) (hb : 1 < b)
+    (h : ∀ k, k ≤ K → b ≤ orbit k n ∧ Q*orbit k n ≤ P*b) : False := by
+  obtain ⟨k,hk,hl | hu⟩ := hc b n hb
+  · have := h k hk; omega
+  · have := h k hk; omega
+
+theorem high_within {P Q K b n : Nat} (hc : ExitClock P Q K) (hb : 1 < b)
+    (h : Kernel b n) : ∃ k, k ≤ K ∧ P*b < Q*orbit k n := by
+  obtain ⟨k,hk,hl | hu⟩ := hc b n hb
+  · have := h k; omega
+  · exact ⟨k,hk,hu⟩
+
+theorem high_window {P Q K b n : Nat} (hc : ExitClock P Q K) (hb : 1 < b)
+    (h : Kernel b n) (t : Nat) :
+    ∃ s, t ≤ s ∧ s ≤ t+K ∧ P*b < Q*orbit s n := by
+  obtain ⟨k,hk,hv⟩ := high_within hc hb (kernel_forward h t)
+  refine ⟨k+t,by omega,by omega,?_⟩
+  rw [orbit_add]
+  exact hv
+
+/-- One distinct high time in each complete (K+1)-point block, using only
+lower survival of the observed prefix. N=0 gives the empty witness family. -/
+theorem finite_survival_witnesses {P Q K b n : Nat} (hc : ExitClock P Q K)
+    (hb : 1 < b) (N : Nat) (h : Survives b ((K+1)*N-1) n) :
+    ∃ f : Fin N → Nat,
+      (∀ q, f q < (K+1)*N ∧ P*b < Q*orbit (f q) n) ∧
+      (∀ a c, f a = f c → a = c) := by
+  classical
+  have span (q : Fin N) : (K+1)*(q.val+1) ≤ (K+1)*N :=
+    Nat.mul_le_mul_left (K+1) (by have := q.isLt; omega)
+  have hw (q : Fin N) : ∃ s,
+      (K+1)*q.val ≤ s ∧ s < (K+1)*(q.val+1) ∧ P*b < Q*orbit s n := by
+    have hs := span q
+    rw [Nat.mul_add, Nat.mul_one] at hs
+    obtain ⟨k,hk,hl | hu⟩ := hc b (orbit ((K+1)*q.val) n) hb
+    · have hlower := h (k+(K+1)*q.val) (by omega)
+      rw [orbit_add] at hlower
+      omega
+    · refine ⟨k+(K+1)*q.val,by omega,?_,?_⟩
+      · rw [Nat.mul_add, Nat.mul_one]; omega
+      · rw [orbit_add]; exact hu
+  let f (q : Fin N) := Classical.choose (hw q)
+  have hf (q : Fin N) :
+      (K+1)*q.val ≤ f q ∧ f q < (K+1)*(q.val+1) ∧ P*b < Q*orbit (f q) n :=
+    Classical.choose_spec (hw q)
+  refine ⟨f,?_,?_⟩
+  · intro q
+    exact ⟨Nat.lt_of_lt_of_le (hf q).2.1 (span q), (hf q).2.2⟩
+  · intro a c he
+    have hv : a.val = c.val := by
+      by_cases hac : a.val < c.val
+      · have hm := Nat.mul_le_mul_left (K+1) (show a.val+1 ≤ c.val by omega)
+        have ht := Nat.lt_of_lt_of_le (hf a).2.1 (Nat.le_trans hm (hf c).1)
+        omega
+      · by_cases hca : c.val < a.val
+        · have hm := Nat.mul_le_mul_left (K+1) (show c.val+1 ≤ a.val by omega)
+          have ht := Nat.lt_of_lt_of_le (hf c).2.1 (Nat.le_trans hm (hf a).1)
+          omega
+        · omega
+    exact Fin.ext hv
+
+theorem kernel_finite_witnesses {P Q K b n : Nat} (hc : ExitClock P Q K)
+    (hb : 1 < b) (h : Kernel b n) (N : Nat) :
+    ∃ f : Fin N → Nat,
+      (∀ q, f q < (K+1)*N ∧ P*b < Q*orbit (f q) n) ∧
+      (∀ a c, f a = f c → a = c) :=
+  finite_survival_witnesses hc hb N (fun k _ => h k)
+
+end Collatz.Exploration.BandClock
diff --git a/Collatz/Exploration/WiderBandArithmetic.lean b/Collatz/Exploration/WiderBandArithmetic.lean
new file mode 100644
index 00000000..a6c5a7fe
--- /dev/null
+++ b/Collatz/Exploration/WiderBandArithmetic.lean
@@ -0,0 +1,4535 @@
+import Collatz.Basic
+
+/-! Generated residue-and-affine certificates for the inclusive ratio-21/4 band.
+Every branch and arithmetic conclusion is independently checked by Lean. -/
+namespace Collatz.Exploration.WiderBandArithmetic
+
+set_option maxHeartbeats 2000000
+set_option linter.unusedVariables false
+
+/-- Exact source residue and full affine trace for branch `0`. -/
+theorem parameters_0
+    (x0 x1 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    : ∃ q : Nat, x0 = 2*q+0 ∧ x1 = 1*q+0 := by
+  let q := x0
+  have p0 : x0 = q := rfl
+  have hstep := r0.1
+  have hparity := r0.2
+  clear r0
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `1`. -/
+theorem parameters_1
+    (x0 x1 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    : ∃ q : Nat, x0 = 2*q+1 ∧ x1 = 6*q+4 := by
+  let q := x0
+  have p0 : x0 = q := rfl
+  have hstep := r0.1
+  have hparity := r0.2
+  clear r0
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `00`. -/
+theorem parameters_00
+    (x0 x1 x2 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    : ∃ q : Nat, x0 = 4*q+0 ∧ x1 = 2*q+0 ∧ x2 = 1*q+0 := by
+  obtain ⟨q,p0,p1⟩ := parameters_0 x0 x1 r0
+  have hstep := r1.1
+  have hparity := r1.2
+  clear r0 r1
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `01`. -/
+theorem parameters_01
+    (x0 x1 x2 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    : ∃ q : Nat, x0 = 4*q+2 ∧ x1 = 2*q+1 ∧ x2 = 6*q+4 := by
+  obtain ⟨q,p0,p1⟩ := parameters_0 x0 x1 r0
+  have hstep := r1.1
+  have hparity := r1.2
+  clear r0 r1
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `10`. -/
+theorem parameters_10
+    (x0 x1 x2 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    : ∃ q : Nat, x0 = 2*q+1 ∧ x1 = 6*q+4 ∧ x2 = 3*q+2 := by
+  obtain ⟨q,p0,p1⟩ := parameters_1 x0 x1 r0
+  have hstep := r1.1
+  have hparity := r1.2
+  clear r0 r1
+  clear hparity
+  refine ⟨q,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `000`. -/
+theorem parameters_000
+    (x0 x1 x2 x3 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    : ∃ q : Nat, x0 = 8*q+0 ∧ x1 = 4*q+0 ∧ x2 = 2*q+0 ∧ x3 = 1*q+0 := by
+  obtain ⟨q,p0,p1,p2⟩ := parameters_00 x0 x1 x2 r0 r1
+  have hstep := r2.1
+  have hparity := r2.2
+  clear r0 r1 r2
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `001`. -/
+theorem parameters_001
+    (x0 x1 x2 x3 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    : ∃ q : Nat, x0 = 8*q+4 ∧ x1 = 4*q+2 ∧ x2 = 2*q+1 ∧ x3 = 6*q+4 := by
+  obtain ⟨q,p0,p1,p2⟩ := parameters_00 x0 x1 x2 r0 r1
+  have hstep := r2.1
+  have hparity := r2.2
+  clear r0 r1 r2
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `010`. -/
+theorem parameters_010
+    (x0 x1 x2 x3 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    : ∃ q : Nat, x0 = 4*q+2 ∧ x1 = 2*q+1 ∧ x2 = 6*q+4 ∧ x3 = 3*q+2 := by
+  obtain ⟨q,p0,p1,p2⟩ := parameters_01 x0 x1 x2 r0 r1
+  have hstep := r2.1
+  have hparity := r2.2
+  clear r0 r1 r2
+  clear hparity
+  refine ⟨q,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `100`. -/
+theorem parameters_100
+    (x0 x1 x2 x3 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    : ∃ q : Nat, x0 = 4*q+1 ∧ x1 = 12*q+4 ∧ x2 = 6*q+2 ∧ x3 = 3*q+1 := by
+  obtain ⟨q,p0,p1,p2⟩ := parameters_10 x0 x1 x2 r0 r1
+  have hstep := r2.1
+  have hparity := r2.2
+  clear r0 r1 r2
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `101`. -/
+theorem parameters_101
+    (x0 x1 x2 x3 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    : ∃ q : Nat, x0 = 4*q+3 ∧ x1 = 12*q+10 ∧ x2 = 6*q+5 ∧ x3 = 18*q+16 := by
+  obtain ⟨q,p0,p1,p2⟩ := parameters_10 x0 x1 x2 r0 r1
+  have hstep := r2.1
+  have hparity := r2.2
+  clear r0 r1 r2
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `0010`. -/
+theorem parameters_0010
+    (x0 x1 x2 x3 x4 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    : ∃ q : Nat, x0 = 8*q+4 ∧ x1 = 4*q+2 ∧ x2 = 2*q+1 ∧ x3 = 6*q+4 ∧ x4 = 3*q+2 := by
+  obtain ⟨q,p0,p1,p2,p3⟩ := parameters_001 x0 x1 x2 x3 r0 r1 r2
+  have hstep := r3.1
+  have hparity := r3.2
+  clear r0 r1 r2 r3
+  clear hparity
+  refine ⟨q,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `0100`. -/
+theorem parameters_0100
+    (x0 x1 x2 x3 x4 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    : ∃ q : Nat, x0 = 8*q+2 ∧ x1 = 4*q+1 ∧ x2 = 12*q+4 ∧ x3 = 6*q+2 ∧ x4 = 3*q+1 := by
+  obtain ⟨q,p0,p1,p2,p3⟩ := parameters_010 x0 x1 x2 x3 r0 r1 r2
+  have hstep := r3.1
+  have hparity := r3.2
+  clear r0 r1 r2 r3
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `0101`. -/
+theorem parameters_0101
+    (x0 x1 x2 x3 x4 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    : ∃ q : Nat, x0 = 8*q+6 ∧ x1 = 4*q+3 ∧ x2 = 12*q+10 ∧ x3 = 6*q+5 ∧ x4 = 18*q+16 := by
+  obtain ⟨q,p0,p1,p2,p3⟩ := parameters_010 x0 x1 x2 x3 r0 r1 r2
+  have hstep := r3.1
+  have hparity := r3.2
+  clear r0 r1 r2 r3
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `1000`. -/
+theorem parameters_1000
+    (x0 x1 x2 x3 x4 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    : ∃ q : Nat, x0 = 8*q+5 ∧ x1 = 24*q+16 ∧ x2 = 12*q+8 ∧ x3 = 6*q+4 ∧ x4 = 3*q+2 := by
+  obtain ⟨q,p0,p1,p2,p3⟩ := parameters_100 x0 x1 x2 x3 r0 r1 r2
+  have hstep := r3.1
+  have hparity := r3.2
+  clear r0 r1 r2 r3
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `1001`. -/
+theorem parameters_1001
+    (x0 x1 x2 x3 x4 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    : ∃ q : Nat, x0 = 8*q+1 ∧ x1 = 24*q+4 ∧ x2 = 12*q+2 ∧ x3 = 6*q+1 ∧ x4 = 18*q+4 := by
+  obtain ⟨q,p0,p1,p2,p3⟩ := parameters_100 x0 x1 x2 x3 r0 r1 r2
+  have hstep := r3.1
+  have hparity := r3.2
+  clear r0 r1 r2 r3
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `1010`. -/
+theorem parameters_1010
+    (x0 x1 x2 x3 x4 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    : ∃ q : Nat, x0 = 4*q+3 ∧ x1 = 12*q+10 ∧ x2 = 6*q+5 ∧ x3 = 18*q+16 ∧ x4 = 9*q+8 := by
+  obtain ⟨q,p0,p1,p2,p3⟩ := parameters_101 x0 x1 x2 x3 r0 r1 r2
+  have hstep := r3.1
+  have hparity := r3.2
+  clear r0 r1 r2 r3
+  clear hparity
+  refine ⟨q,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `00100`. -/
+theorem parameters_00100
+    (x0 x1 x2 x3 x4 x5 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    : ∃ q : Nat, x0 = 16*q+4 ∧ x1 = 8*q+2 ∧ x2 = 4*q+1 ∧ x3 = 12*q+4 ∧ x4 = 6*q+2 ∧ x5 = 3*q+1 := by
+  obtain ⟨q,p0,p1,p2,p3,p4⟩ := parameters_0010 x0 x1 x2 x3 x4 r0 r1 r2 r3
+  have hstep := r4.1
+  have hparity := r4.2
+  clear r0 r1 r2 r3 r4
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `00101`. -/
+theorem parameters_00101
+    (x0 x1 x2 x3 x4 x5 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    : ∃ q : Nat, x0 = 16*q+12 ∧ x1 = 8*q+6 ∧ x2 = 4*q+3 ∧ x3 = 12*q+10 ∧ x4 = 6*q+5 ∧ x5 = 18*q+16 := by
+  obtain ⟨q,p0,p1,p2,p3,p4⟩ := parameters_0010 x0 x1 x2 x3 x4 r0 r1 r2 r3
+  have hstep := r4.1
+  have hparity := r4.2
+  clear r0 r1 r2 r3 r4
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `01000`. -/
+theorem parameters_01000
+    (x0 x1 x2 x3 x4 x5 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    : ∃ q : Nat, x0 = 16*q+10 ∧ x1 = 8*q+5 ∧ x2 = 24*q+16 ∧ x3 = 12*q+8 ∧ x4 = 6*q+4 ∧ x5 = 3*q+2 := by
+  obtain ⟨q,p0,p1,p2,p3,p4⟩ := parameters_0100 x0 x1 x2 x3 x4 r0 r1 r2 r3
+  have hstep := r4.1
+  have hparity := r4.2
+  clear r0 r1 r2 r3 r4
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `01001`. -/
+theorem parameters_01001
+    (x0 x1 x2 x3 x4 x5 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    : ∃ q : Nat, x0 = 16*q+2 ∧ x1 = 8*q+1 ∧ x2 = 24*q+4 ∧ x3 = 12*q+2 ∧ x4 = 6*q+1 ∧ x5 = 18*q+4 := by
+  obtain ⟨q,p0,p1,p2,p3,p4⟩ := parameters_0100 x0 x1 x2 x3 x4 r0 r1 r2 r3
+  have hstep := r4.1
+  have hparity := r4.2
+  clear r0 r1 r2 r3 r4
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `01010`. -/
+theorem parameters_01010
+    (x0 x1 x2 x3 x4 x5 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    : ∃ q : Nat, x0 = 8*q+6 ∧ x1 = 4*q+3 ∧ x2 = 12*q+10 ∧ x3 = 6*q+5 ∧ x4 = 18*q+16 ∧ x5 = 9*q+8 := by
+  obtain ⟨q,p0,p1,p2,p3,p4⟩ := parameters_0101 x0 x1 x2 x3 x4 r0 r1 r2 r3
+  have hstep := r4.1
+  have hparity := r4.2
+  clear r0 r1 r2 r3 r4
+  clear hparity
+  refine ⟨q,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `10010`. -/
+theorem parameters_10010
+    (x0 x1 x2 x3 x4 x5 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    : ∃ q : Nat, x0 = 8*q+1 ∧ x1 = 24*q+4 ∧ x2 = 12*q+2 ∧ x3 = 6*q+1 ∧ x4 = 18*q+4 ∧ x5 = 9*q+2 := by
+  obtain ⟨q,p0,p1,p2,p3,p4⟩ := parameters_1001 x0 x1 x2 x3 x4 r0 r1 r2 r3
+  have hstep := r4.1
+  have hparity := r4.2
+  clear r0 r1 r2 r3 r4
+  clear hparity
+  refine ⟨q,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `10100`. -/
+theorem parameters_10100
+    (x0 x1 x2 x3 x4 x5 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    : ∃ q : Nat, x0 = 8*q+3 ∧ x1 = 24*q+10 ∧ x2 = 12*q+5 ∧ x3 = 36*q+16 ∧ x4 = 18*q+8 ∧ x5 = 9*q+4 := by
+  obtain ⟨q,p0,p1,p2,p3,p4⟩ := parameters_1010 x0 x1 x2 x3 x4 r0 r1 r2 r3
+  have hstep := r4.1
+  have hparity := r4.2
+  clear r0 r1 r2 r3 r4
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `10101`. -/
+theorem parameters_10101
+    (x0 x1 x2 x3 x4 x5 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    : ∃ q : Nat, x0 = 8*q+7 ∧ x1 = 24*q+22 ∧ x2 = 12*q+11 ∧ x3 = 36*q+34 ∧ x4 = 18*q+17 ∧ x5 = 54*q+52 := by
+  obtain ⟨q,p0,p1,p2,p3,p4⟩ := parameters_1010 x0 x1 x2 x3 x4 r0 r1 r2 r3
+  have hstep := r4.1
+  have hparity := r4.2
+  clear r0 r1 r2 r3 r4
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `001000`. -/
+theorem parameters_001000
+    (x0 x1 x2 x3 x4 x5 x6 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    : ∃ q : Nat, x0 = 32*q+20 ∧ x1 = 16*q+10 ∧ x2 = 8*q+5 ∧ x3 = 24*q+16 ∧ x4 = 12*q+8 ∧ x5 = 6*q+4 ∧ x6 = 3*q+2 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5⟩ := parameters_00100 x0 x1 x2 x3 x4 x5 r0 r1 r2 r3 r4
+  have hstep := r5.1
+  have hparity := r5.2
+  clear r0 r1 r2 r3 r4 r5
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `001001`. -/
+theorem parameters_001001
+    (x0 x1 x2 x3 x4 x5 x6 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    : ∃ q : Nat, x0 = 32*q+4 ∧ x1 = 16*q+2 ∧ x2 = 8*q+1 ∧ x3 = 24*q+4 ∧ x4 = 12*q+2 ∧ x5 = 6*q+1 ∧ x6 = 18*q+4 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5⟩ := parameters_00100 x0 x1 x2 x3 x4 x5 r0 r1 r2 r3 r4
+  have hstep := r5.1
+  have hparity := r5.2
+  clear r0 r1 r2 r3 r4 r5
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `001010`. -/
+theorem parameters_001010
+    (x0 x1 x2 x3 x4 x5 x6 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    : ∃ q : Nat, x0 = 16*q+12 ∧ x1 = 8*q+6 ∧ x2 = 4*q+3 ∧ x3 = 12*q+10 ∧ x4 = 6*q+5 ∧ x5 = 18*q+16 ∧ x6 = 9*q+8 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5⟩ := parameters_00101 x0 x1 x2 x3 x4 x5 r0 r1 r2 r3 r4
+  have hstep := r5.1
+  have hparity := r5.2
+  clear r0 r1 r2 r3 r4 r5
+  clear hparity
+  refine ⟨q,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `010010`. -/
+theorem parameters_010010
+    (x0 x1 x2 x3 x4 x5 x6 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    : ∃ q : Nat, x0 = 16*q+2 ∧ x1 = 8*q+1 ∧ x2 = 24*q+4 ∧ x3 = 12*q+2 ∧ x4 = 6*q+1 ∧ x5 = 18*q+4 ∧ x6 = 9*q+2 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5⟩ := parameters_01001 x0 x1 x2 x3 x4 x5 r0 r1 r2 r3 r4
+  have hstep := r5.1
+  have hparity := r5.2
+  clear r0 r1 r2 r3 r4 r5
+  clear hparity
+  refine ⟨q,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `010100`. -/
+theorem parameters_010100
+    (x0 x1 x2 x3 x4 x5 x6 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    : ∃ q : Nat, x0 = 16*q+6 ∧ x1 = 8*q+3 ∧ x2 = 24*q+10 ∧ x3 = 12*q+5 ∧ x4 = 36*q+16 ∧ x5 = 18*q+8 ∧ x6 = 9*q+4 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5⟩ := parameters_01010 x0 x1 x2 x3 x4 x5 r0 r1 r2 r3 r4
+  have hstep := r5.1
+  have hparity := r5.2
+  clear r0 r1 r2 r3 r4 r5
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `010101`. -/
+theorem parameters_010101
+    (x0 x1 x2 x3 x4 x5 x6 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    : ∃ q : Nat, x0 = 16*q+14 ∧ x1 = 8*q+7 ∧ x2 = 24*q+22 ∧ x3 = 12*q+11 ∧ x4 = 36*q+34 ∧ x5 = 18*q+17 ∧ x6 = 54*q+52 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5⟩ := parameters_01010 x0 x1 x2 x3 x4 x5 r0 r1 r2 r3 r4
+  have hstep := r5.1
+  have hparity := r5.2
+  clear r0 r1 r2 r3 r4 r5
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `100100`. -/
+theorem parameters_100100
+    (x0 x1 x2 x3 x4 x5 x6 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    : ∃ q : Nat, x0 = 16*q+1 ∧ x1 = 48*q+4 ∧ x2 = 24*q+2 ∧ x3 = 12*q+1 ∧ x4 = 36*q+4 ∧ x5 = 18*q+2 ∧ x6 = 9*q+1 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5⟩ := parameters_10010 x0 x1 x2 x3 x4 x5 r0 r1 r2 r3 r4
+  have hstep := r5.1
+  have hparity := r5.2
+  clear r0 r1 r2 r3 r4 r5
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `100101`. -/
+theorem parameters_100101
+    (x0 x1 x2 x3 x4 x5 x6 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    : ∃ q : Nat, x0 = 16*q+9 ∧ x1 = 48*q+28 ∧ x2 = 24*q+14 ∧ x3 = 12*q+7 ∧ x4 = 36*q+22 ∧ x5 = 18*q+11 ∧ x6 = 54*q+34 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5⟩ := parameters_10010 x0 x1 x2 x3 x4 x5 r0 r1 r2 r3 r4
+  have hstep := r5.1
+  have hparity := r5.2
+  clear r0 r1 r2 r3 r4 r5
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `101000`. -/
+theorem parameters_101000
+    (x0 x1 x2 x3 x4 x5 x6 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    : ∃ q : Nat, x0 = 16*q+3 ∧ x1 = 48*q+10 ∧ x2 = 24*q+5 ∧ x3 = 72*q+16 ∧ x4 = 36*q+8 ∧ x5 = 18*q+4 ∧ x6 = 9*q+2 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5⟩ := parameters_10100 x0 x1 x2 x3 x4 x5 r0 r1 r2 r3 r4
+  have hstep := r5.1
+  have hparity := r5.2
+  clear r0 r1 r2 r3 r4 r5
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `101001`. -/
+theorem parameters_101001
+    (x0 x1 x2 x3 x4 x5 x6 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    : ∃ q : Nat, x0 = 16*q+11 ∧ x1 = 48*q+34 ∧ x2 = 24*q+17 ∧ x3 = 72*q+52 ∧ x4 = 36*q+26 ∧ x5 = 18*q+13 ∧ x6 = 54*q+40 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5⟩ := parameters_10100 x0 x1 x2 x3 x4 x5 r0 r1 r2 r3 r4
+  have hstep := r5.1
+  have hparity := r5.2
+  clear r0 r1 r2 r3 r4 r5
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `0010010`. -/
+theorem parameters_0010010
+    (x0 x1 x2 x3 x4 x5 x6 x7 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    : ∃ q : Nat, x0 = 32*q+4 ∧ x1 = 16*q+2 ∧ x2 = 8*q+1 ∧ x3 = 24*q+4 ∧ x4 = 12*q+2 ∧ x5 = 6*q+1 ∧ x6 = 18*q+4 ∧ x7 = 9*q+2 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6⟩ := parameters_001001 x0 x1 x2 x3 x4 x5 x6 r0 r1 r2 r3 r4 r5
+  have hstep := r6.1
+  have hparity := r6.2
+  clear r0 r1 r2 r3 r4 r5 r6
+  clear hparity
+  refine ⟨q,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `0010100`. -/
+theorem parameters_0010100
+    (x0 x1 x2 x3 x4 x5 x6 x7 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    : ∃ q : Nat, x0 = 32*q+12 ∧ x1 = 16*q+6 ∧ x2 = 8*q+3 ∧ x3 = 24*q+10 ∧ x4 = 12*q+5 ∧ x5 = 36*q+16 ∧ x6 = 18*q+8 ∧ x7 = 9*q+4 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6⟩ := parameters_001010 x0 x1 x2 x3 x4 x5 x6 r0 r1 r2 r3 r4 r5
+  have hstep := r6.1
+  have hparity := r6.2
+  clear r0 r1 r2 r3 r4 r5 r6
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `0010101`. -/
+theorem parameters_0010101
+    (x0 x1 x2 x3 x4 x5 x6 x7 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    : ∃ q : Nat, x0 = 32*q+28 ∧ x1 = 16*q+14 ∧ x2 = 8*q+7 ∧ x3 = 24*q+22 ∧ x4 = 12*q+11 ∧ x5 = 36*q+34 ∧ x6 = 18*q+17 ∧ x7 = 54*q+52 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6⟩ := parameters_001010 x0 x1 x2 x3 x4 x5 x6 r0 r1 r2 r3 r4 r5
+  have hstep := r6.1
+  have hparity := r6.2
+  clear r0 r1 r2 r3 r4 r5 r6
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `0100100`. -/
+theorem parameters_0100100
+    (x0 x1 x2 x3 x4 x5 x6 x7 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    : ∃ q : Nat, x0 = 32*q+2 ∧ x1 = 16*q+1 ∧ x2 = 48*q+4 ∧ x3 = 24*q+2 ∧ x4 = 12*q+1 ∧ x5 = 36*q+4 ∧ x6 = 18*q+2 ∧ x7 = 9*q+1 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6⟩ := parameters_010010 x0 x1 x2 x3 x4 x5 x6 r0 r1 r2 r3 r4 r5
+  have hstep := r6.1
+  have hparity := r6.2
+  clear r0 r1 r2 r3 r4 r5 r6
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `0100101`. -/
+theorem parameters_0100101
+    (x0 x1 x2 x3 x4 x5 x6 x7 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    : ∃ q : Nat, x0 = 32*q+18 ∧ x1 = 16*q+9 ∧ x2 = 48*q+28 ∧ x3 = 24*q+14 ∧ x4 = 12*q+7 ∧ x5 = 36*q+22 ∧ x6 = 18*q+11 ∧ x7 = 54*q+34 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6⟩ := parameters_010010 x0 x1 x2 x3 x4 x5 x6 r0 r1 r2 r3 r4 r5
+  have hstep := r6.1
+  have hparity := r6.2
+  clear r0 r1 r2 r3 r4 r5 r6
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `0101000`. -/
+theorem parameters_0101000
+    (x0 x1 x2 x3 x4 x5 x6 x7 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    : ∃ q : Nat, x0 = 32*q+6 ∧ x1 = 16*q+3 ∧ x2 = 48*q+10 ∧ x3 = 24*q+5 ∧ x4 = 72*q+16 ∧ x5 = 36*q+8 ∧ x6 = 18*q+4 ∧ x7 = 9*q+2 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6⟩ := parameters_010100 x0 x1 x2 x3 x4 x5 x6 r0 r1 r2 r3 r4 r5
+  have hstep := r6.1
+  have hparity := r6.2
+  clear r0 r1 r2 r3 r4 r5 r6
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `0101001`. -/
+theorem parameters_0101001
+    (x0 x1 x2 x3 x4 x5 x6 x7 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    : ∃ q : Nat, x0 = 32*q+22 ∧ x1 = 16*q+11 ∧ x2 = 48*q+34 ∧ x3 = 24*q+17 ∧ x4 = 72*q+52 ∧ x5 = 36*q+26 ∧ x6 = 18*q+13 ∧ x7 = 54*q+40 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6⟩ := parameters_010100 x0 x1 x2 x3 x4 x5 x6 r0 r1 r2 r3 r4 r5
+  have hstep := r6.1
+  have hparity := r6.2
+  clear r0 r1 r2 r3 r4 r5 r6
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `1001000`. -/
+theorem parameters_1001000
+    (x0 x1 x2 x3 x4 x5 x6 x7 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    : ∃ q : Nat, x0 = 32*q+17 ∧ x1 = 96*q+52 ∧ x2 = 48*q+26 ∧ x3 = 24*q+13 ∧ x4 = 72*q+40 ∧ x5 = 36*q+20 ∧ x6 = 18*q+10 ∧ x7 = 9*q+5 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6⟩ := parameters_100100 x0 x1 x2 x3 x4 x5 x6 r0 r1 r2 r3 r4 r5
+  have hstep := r6.1
+  have hparity := r6.2
+  clear r0 r1 r2 r3 r4 r5 r6
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `1001001`. -/
+theorem parameters_1001001
+    (x0 x1 x2 x3 x4 x5 x6 x7 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    : ∃ q : Nat, x0 = 32*q+1 ∧ x1 = 96*q+4 ∧ x2 = 48*q+2 ∧ x3 = 24*q+1 ∧ x4 = 72*q+4 ∧ x5 = 36*q+2 ∧ x6 = 18*q+1 ∧ x7 = 54*q+4 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6⟩ := parameters_100100 x0 x1 x2 x3 x4 x5 x6 r0 r1 r2 r3 r4 r5
+  have hstep := r6.1
+  have hparity := r6.2
+  clear r0 r1 r2 r3 r4 r5 r6
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `1001010`. -/
+theorem parameters_1001010
+    (x0 x1 x2 x3 x4 x5 x6 x7 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    : ∃ q : Nat, x0 = 16*q+9 ∧ x1 = 48*q+28 ∧ x2 = 24*q+14 ∧ x3 = 12*q+7 ∧ x4 = 36*q+22 ∧ x5 = 18*q+11 ∧ x6 = 54*q+34 ∧ x7 = 27*q+17 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6⟩ := parameters_100101 x0 x1 x2 x3 x4 x5 x6 r0 r1 r2 r3 r4 r5
+  have hstep := r6.1
+  have hparity := r6.2
+  clear r0 r1 r2 r3 r4 r5 r6
+  clear hparity
+  refine ⟨q,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `1010010`. -/
+theorem parameters_1010010
+    (x0 x1 x2 x3 x4 x5 x6 x7 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    : ∃ q : Nat, x0 = 16*q+11 ∧ x1 = 48*q+34 ∧ x2 = 24*q+17 ∧ x3 = 72*q+52 ∧ x4 = 36*q+26 ∧ x5 = 18*q+13 ∧ x6 = 54*q+40 ∧ x7 = 27*q+20 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6⟩ := parameters_101001 x0 x1 x2 x3 x4 x5 x6 r0 r1 r2 r3 r4 r5
+  have hstep := r6.1
+  have hparity := r6.2
+  clear r0 r1 r2 r3 r4 r5 r6
+  clear hparity
+  refine ⟨q,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `00100100`. -/
+theorem parameters_00100100
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    : ∃ q : Nat, x0 = 64*q+4 ∧ x1 = 32*q+2 ∧ x2 = 16*q+1 ∧ x3 = 48*q+4 ∧ x4 = 24*q+2 ∧ x5 = 12*q+1 ∧ x6 = 36*q+4 ∧ x7 = 18*q+2 ∧ x8 = 9*q+1 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7⟩ := parameters_0010010 x0 x1 x2 x3 x4 x5 x6 x7 r0 r1 r2 r3 r4 r5 r6
+  have hstep := r7.1
+  have hparity := r7.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `00100101`. -/
+theorem parameters_00100101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    : ∃ q : Nat, x0 = 64*q+36 ∧ x1 = 32*q+18 ∧ x2 = 16*q+9 ∧ x3 = 48*q+28 ∧ x4 = 24*q+14 ∧ x5 = 12*q+7 ∧ x6 = 36*q+22 ∧ x7 = 18*q+11 ∧ x8 = 54*q+34 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7⟩ := parameters_0010010 x0 x1 x2 x3 x4 x5 x6 x7 r0 r1 r2 r3 r4 r5 r6
+  have hstep := r7.1
+  have hparity := r7.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `00101000`. -/
+theorem parameters_00101000
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    : ∃ q : Nat, x0 = 64*q+12 ∧ x1 = 32*q+6 ∧ x2 = 16*q+3 ∧ x3 = 48*q+10 ∧ x4 = 24*q+5 ∧ x5 = 72*q+16 ∧ x6 = 36*q+8 ∧ x7 = 18*q+4 ∧ x8 = 9*q+2 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7⟩ := parameters_0010100 x0 x1 x2 x3 x4 x5 x6 x7 r0 r1 r2 r3 r4 r5 r6
+  have hstep := r7.1
+  have hparity := r7.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `00101001`. -/
+theorem parameters_00101001
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    : ∃ q : Nat, x0 = 64*q+44 ∧ x1 = 32*q+22 ∧ x2 = 16*q+11 ∧ x3 = 48*q+34 ∧ x4 = 24*q+17 ∧ x5 = 72*q+52 ∧ x6 = 36*q+26 ∧ x7 = 18*q+13 ∧ x8 = 54*q+40 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7⟩ := parameters_0010100 x0 x1 x2 x3 x4 x5 x6 x7 r0 r1 r2 r3 r4 r5 r6
+  have hstep := r7.1
+  have hparity := r7.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `01001000`. -/
+theorem parameters_01001000
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    : ∃ q : Nat, x0 = 64*q+34 ∧ x1 = 32*q+17 ∧ x2 = 96*q+52 ∧ x3 = 48*q+26 ∧ x4 = 24*q+13 ∧ x5 = 72*q+40 ∧ x6 = 36*q+20 ∧ x7 = 18*q+10 ∧ x8 = 9*q+5 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7⟩ := parameters_0100100 x0 x1 x2 x3 x4 x5 x6 x7 r0 r1 r2 r3 r4 r5 r6
+  have hstep := r7.1
+  have hparity := r7.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `01001001`. -/
+theorem parameters_01001001
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    : ∃ q : Nat, x0 = 64*q+2 ∧ x1 = 32*q+1 ∧ x2 = 96*q+4 ∧ x3 = 48*q+2 ∧ x4 = 24*q+1 ∧ x5 = 72*q+4 ∧ x6 = 36*q+2 ∧ x7 = 18*q+1 ∧ x8 = 54*q+4 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7⟩ := parameters_0100100 x0 x1 x2 x3 x4 x5 x6 x7 r0 r1 r2 r3 r4 r5 r6
+  have hstep := r7.1
+  have hparity := r7.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `01001010`. -/
+theorem parameters_01001010
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    : ∃ q : Nat, x0 = 32*q+18 ∧ x1 = 16*q+9 ∧ x2 = 48*q+28 ∧ x3 = 24*q+14 ∧ x4 = 12*q+7 ∧ x5 = 36*q+22 ∧ x6 = 18*q+11 ∧ x7 = 54*q+34 ∧ x8 = 27*q+17 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7⟩ := parameters_0100101 x0 x1 x2 x3 x4 x5 x6 x7 r0 r1 r2 r3 r4 r5 r6
+  have hstep := r7.1
+  have hparity := r7.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7
+  clear hparity
+  refine ⟨q,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `01010010`. -/
+theorem parameters_01010010
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    : ∃ q : Nat, x0 = 32*q+22 ∧ x1 = 16*q+11 ∧ x2 = 48*q+34 ∧ x3 = 24*q+17 ∧ x4 = 72*q+52 ∧ x5 = 36*q+26 ∧ x6 = 18*q+13 ∧ x7 = 54*q+40 ∧ x8 = 27*q+20 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7⟩ := parameters_0101001 x0 x1 x2 x3 x4 x5 x6 x7 r0 r1 r2 r3 r4 r5 r6
+  have hstep := r7.1
+  have hparity := r7.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7
+  clear hparity
+  refine ⟨q,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `10010100`. -/
+theorem parameters_10010100
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    : ∃ q : Nat, x0 = 32*q+25 ∧ x1 = 96*q+76 ∧ x2 = 48*q+38 ∧ x3 = 24*q+19 ∧ x4 = 72*q+58 ∧ x5 = 36*q+29 ∧ x6 = 108*q+88 ∧ x7 = 54*q+44 ∧ x8 = 27*q+22 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7⟩ := parameters_1001010 x0 x1 x2 x3 x4 x5 x6 x7 r0 r1 r2 r3 r4 r5 r6
+  have hstep := r7.1
+  have hparity := r7.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `10010101`. -/
+theorem parameters_10010101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    : ∃ q : Nat, x0 = 32*q+9 ∧ x1 = 96*q+28 ∧ x2 = 48*q+14 ∧ x3 = 24*q+7 ∧ x4 = 72*q+22 ∧ x5 = 36*q+11 ∧ x6 = 108*q+34 ∧ x7 = 54*q+17 ∧ x8 = 162*q+52 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7⟩ := parameters_1001010 x0 x1 x2 x3 x4 x5 x6 x7 r0 r1 r2 r3 r4 r5 r6
+  have hstep := r7.1
+  have hparity := r7.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `10100100`. -/
+theorem parameters_10100100
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    : ∃ q : Nat, x0 = 32*q+11 ∧ x1 = 96*q+34 ∧ x2 = 48*q+17 ∧ x3 = 144*q+52 ∧ x4 = 72*q+26 ∧ x5 = 36*q+13 ∧ x6 = 108*q+40 ∧ x7 = 54*q+20 ∧ x8 = 27*q+10 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7⟩ := parameters_1010010 x0 x1 x2 x3 x4 x5 x6 x7 r0 r1 r2 r3 r4 r5 r6
+  have hstep := r7.1
+  have hparity := r7.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `10100101`. -/
+theorem parameters_10100101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    : ∃ q : Nat, x0 = 32*q+27 ∧ x1 = 96*q+82 ∧ x2 = 48*q+41 ∧ x3 = 144*q+124 ∧ x4 = 72*q+62 ∧ x5 = 36*q+31 ∧ x6 = 108*q+94 ∧ x7 = 54*q+47 ∧ x8 = 162*q+142 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7⟩ := parameters_1010010 x0 x1 x2 x3 x4 x5 x6 x7 r0 r1 r2 r3 r4 r5 r6
+  have hstep := r7.1
+  have hparity := r7.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `001001010`. -/
+theorem parameters_001001010
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    : ∃ q : Nat, x0 = 64*q+36 ∧ x1 = 32*q+18 ∧ x2 = 16*q+9 ∧ x3 = 48*q+28 ∧ x4 = 24*q+14 ∧ x5 = 12*q+7 ∧ x6 = 36*q+22 ∧ x7 = 18*q+11 ∧ x8 = 54*q+34 ∧ x9 = 27*q+17 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8⟩ := parameters_00100101 x0 x1 x2 x3 x4 x5 x6 x7 x8 r0 r1 r2 r3 r4 r5 r6 r7
+  have hstep := r8.1
+  have hparity := r8.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8
+  clear hparity
+  refine ⟨q,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `001010010`. -/
+theorem parameters_001010010
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    : ∃ q : Nat, x0 = 64*q+44 ∧ x1 = 32*q+22 ∧ x2 = 16*q+11 ∧ x3 = 48*q+34 ∧ x4 = 24*q+17 ∧ x5 = 72*q+52 ∧ x6 = 36*q+26 ∧ x7 = 18*q+13 ∧ x8 = 54*q+40 ∧ x9 = 27*q+20 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8⟩ := parameters_00101001 x0 x1 x2 x3 x4 x5 x6 x7 x8 r0 r1 r2 r3 r4 r5 r6 r7
+  have hstep := r8.1
+  have hparity := r8.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8
+  clear hparity
+  refine ⟨q,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `010010100`. -/
+theorem parameters_010010100
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    : ∃ q : Nat, x0 = 64*q+50 ∧ x1 = 32*q+25 ∧ x2 = 96*q+76 ∧ x3 = 48*q+38 ∧ x4 = 24*q+19 ∧ x5 = 72*q+58 ∧ x6 = 36*q+29 ∧ x7 = 108*q+88 ∧ x8 = 54*q+44 ∧ x9 = 27*q+22 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8⟩ := parameters_01001010 x0 x1 x2 x3 x4 x5 x6 x7 x8 r0 r1 r2 r3 r4 r5 r6 r7
+  have hstep := r8.1
+  have hparity := r8.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `010010101`. -/
+theorem parameters_010010101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    : ∃ q : Nat, x0 = 64*q+18 ∧ x1 = 32*q+9 ∧ x2 = 96*q+28 ∧ x3 = 48*q+14 ∧ x4 = 24*q+7 ∧ x5 = 72*q+22 ∧ x6 = 36*q+11 ∧ x7 = 108*q+34 ∧ x8 = 54*q+17 ∧ x9 = 162*q+52 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8⟩ := parameters_01001010 x0 x1 x2 x3 x4 x5 x6 x7 x8 r0 r1 r2 r3 r4 r5 r6 r7
+  have hstep := r8.1
+  have hparity := r8.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `010100100`. -/
+theorem parameters_010100100
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    : ∃ q : Nat, x0 = 64*q+22 ∧ x1 = 32*q+11 ∧ x2 = 96*q+34 ∧ x3 = 48*q+17 ∧ x4 = 144*q+52 ∧ x5 = 72*q+26 ∧ x6 = 36*q+13 ∧ x7 = 108*q+40 ∧ x8 = 54*q+20 ∧ x9 = 27*q+10 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8⟩ := parameters_01010010 x0 x1 x2 x3 x4 x5 x6 x7 x8 r0 r1 r2 r3 r4 r5 r6 r7
+  have hstep := r8.1
+  have hparity := r8.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `010100101`. -/
+theorem parameters_010100101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    : ∃ q : Nat, x0 = 64*q+54 ∧ x1 = 32*q+27 ∧ x2 = 96*q+82 ∧ x3 = 48*q+41 ∧ x4 = 144*q+124 ∧ x5 = 72*q+62 ∧ x6 = 36*q+31 ∧ x7 = 108*q+94 ∧ x8 = 54*q+47 ∧ x9 = 162*q+142 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8⟩ := parameters_01010010 x0 x1 x2 x3 x4 x5 x6 x7 x8 r0 r1 r2 r3 r4 r5 r6 r7
+  have hstep := r8.1
+  have hparity := r8.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `100101000`. -/
+theorem parameters_100101000
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    : ∃ q : Nat, x0 = 64*q+25 ∧ x1 = 192*q+76 ∧ x2 = 96*q+38 ∧ x3 = 48*q+19 ∧ x4 = 144*q+58 ∧ x5 = 72*q+29 ∧ x6 = 216*q+88 ∧ x7 = 108*q+44 ∧ x8 = 54*q+22 ∧ x9 = 27*q+11 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8⟩ := parameters_10010100 x0 x1 x2 x3 x4 x5 x6 x7 x8 r0 r1 r2 r3 r4 r5 r6 r7
+  have hstep := r8.1
+  have hparity := r8.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `100101001`. -/
+theorem parameters_100101001
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    : ∃ q : Nat, x0 = 64*q+57 ∧ x1 = 192*q+172 ∧ x2 = 96*q+86 ∧ x3 = 48*q+43 ∧ x4 = 144*q+130 ∧ x5 = 72*q+65 ∧ x6 = 216*q+196 ∧ x7 = 108*q+98 ∧ x8 = 54*q+49 ∧ x9 = 162*q+148 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8⟩ := parameters_10010100 x0 x1 x2 x3 x4 x5 x6 x7 x8 r0 r1 r2 r3 r4 r5 r6 r7
+  have hstep := r8.1
+  have hparity := r8.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `101001000`. -/
+theorem parameters_101001000
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    : ∃ q : Nat, x0 = 64*q+11 ∧ x1 = 192*q+34 ∧ x2 = 96*q+17 ∧ x3 = 288*q+52 ∧ x4 = 144*q+26 ∧ x5 = 72*q+13 ∧ x6 = 216*q+40 ∧ x7 = 108*q+20 ∧ x8 = 54*q+10 ∧ x9 = 27*q+5 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8⟩ := parameters_10100100 x0 x1 x2 x3 x4 x5 x6 x7 x8 r0 r1 r2 r3 r4 r5 r6 r7
+  have hstep := r8.1
+  have hparity := r8.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `101001001`. -/
+theorem parameters_101001001
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    : ∃ q : Nat, x0 = 64*q+43 ∧ x1 = 192*q+130 ∧ x2 = 96*q+65 ∧ x3 = 288*q+196 ∧ x4 = 144*q+98 ∧ x5 = 72*q+49 ∧ x6 = 216*q+148 ∧ x7 = 108*q+74 ∧ x8 = 54*q+37 ∧ x9 = 162*q+112 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8⟩ := parameters_10100100 x0 x1 x2 x3 x4 x5 x6 x7 x8 r0 r1 r2 r3 r4 r5 r6 r7
+  have hstep := r8.1
+  have hparity := r8.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `101001010`. -/
+theorem parameters_101001010
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    : ∃ q : Nat, x0 = 32*q+27 ∧ x1 = 96*q+82 ∧ x2 = 48*q+41 ∧ x3 = 144*q+124 ∧ x4 = 72*q+62 ∧ x5 = 36*q+31 ∧ x6 = 108*q+94 ∧ x7 = 54*q+47 ∧ x8 = 162*q+142 ∧ x9 = 81*q+71 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8⟩ := parameters_10100101 x0 x1 x2 x3 x4 x5 x6 x7 x8 r0 r1 r2 r3 r4 r5 r6 r7
+  have hstep := r8.1
+  have hparity := r8.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8
+  clear hparity
+  refine ⟨q,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `0010010100`. -/
+theorem parameters_0010010100
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    : ∃ q : Nat, x0 = 128*q+100 ∧ x1 = 64*q+50 ∧ x2 = 32*q+25 ∧ x3 = 96*q+76 ∧ x4 = 48*q+38 ∧ x5 = 24*q+19 ∧ x6 = 72*q+58 ∧ x7 = 36*q+29 ∧ x8 = 108*q+88 ∧ x9 = 54*q+44 ∧ x10 = 27*q+22 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9⟩ := parameters_001001010 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 r0 r1 r2 r3 r4 r5 r6 r7 r8
+  have hstep := r9.1
+  have hparity := r9.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `0010010101`. -/
+theorem parameters_0010010101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    : ∃ q : Nat, x0 = 128*q+36 ∧ x1 = 64*q+18 ∧ x2 = 32*q+9 ∧ x3 = 96*q+28 ∧ x4 = 48*q+14 ∧ x5 = 24*q+7 ∧ x6 = 72*q+22 ∧ x7 = 36*q+11 ∧ x8 = 108*q+34 ∧ x9 = 54*q+17 ∧ x10 = 162*q+52 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9⟩ := parameters_001001010 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 r0 r1 r2 r3 r4 r5 r6 r7 r8
+  have hstep := r9.1
+  have hparity := r9.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `0010100100`. -/
+theorem parameters_0010100100
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    : ∃ q : Nat, x0 = 128*q+44 ∧ x1 = 64*q+22 ∧ x2 = 32*q+11 ∧ x3 = 96*q+34 ∧ x4 = 48*q+17 ∧ x5 = 144*q+52 ∧ x6 = 72*q+26 ∧ x7 = 36*q+13 ∧ x8 = 108*q+40 ∧ x9 = 54*q+20 ∧ x10 = 27*q+10 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9⟩ := parameters_001010010 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 r0 r1 r2 r3 r4 r5 r6 r7 r8
+  have hstep := r9.1
+  have hparity := r9.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `0010100101`. -/
+theorem parameters_0010100101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    : ∃ q : Nat, x0 = 128*q+108 ∧ x1 = 64*q+54 ∧ x2 = 32*q+27 ∧ x3 = 96*q+82 ∧ x4 = 48*q+41 ∧ x5 = 144*q+124 ∧ x6 = 72*q+62 ∧ x7 = 36*q+31 ∧ x8 = 108*q+94 ∧ x9 = 54*q+47 ∧ x10 = 162*q+142 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9⟩ := parameters_001010010 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 r0 r1 r2 r3 r4 r5 r6 r7 r8
+  have hstep := r9.1
+  have hparity := r9.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `0100101000`. -/
+theorem parameters_0100101000
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    : ∃ q : Nat, x0 = 128*q+50 ∧ x1 = 64*q+25 ∧ x2 = 192*q+76 ∧ x3 = 96*q+38 ∧ x4 = 48*q+19 ∧ x5 = 144*q+58 ∧ x6 = 72*q+29 ∧ x7 = 216*q+88 ∧ x8 = 108*q+44 ∧ x9 = 54*q+22 ∧ x10 = 27*q+11 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9⟩ := parameters_010010100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 r0 r1 r2 r3 r4 r5 r6 r7 r8
+  have hstep := r9.1
+  have hparity := r9.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `0100101001`. -/
+theorem parameters_0100101001
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    : ∃ q : Nat, x0 = 128*q+114 ∧ x1 = 64*q+57 ∧ x2 = 192*q+172 ∧ x3 = 96*q+86 ∧ x4 = 48*q+43 ∧ x5 = 144*q+130 ∧ x6 = 72*q+65 ∧ x7 = 216*q+196 ∧ x8 = 108*q+98 ∧ x9 = 54*q+49 ∧ x10 = 162*q+148 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9⟩ := parameters_010010100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 r0 r1 r2 r3 r4 r5 r6 r7 r8
+  have hstep := r9.1
+  have hparity := r9.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `0101001000`. -/
+theorem parameters_0101001000
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    : ∃ q : Nat, x0 = 128*q+22 ∧ x1 = 64*q+11 ∧ x2 = 192*q+34 ∧ x3 = 96*q+17 ∧ x4 = 288*q+52 ∧ x5 = 144*q+26 ∧ x6 = 72*q+13 ∧ x7 = 216*q+40 ∧ x8 = 108*q+20 ∧ x9 = 54*q+10 ∧ x10 = 27*q+5 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9⟩ := parameters_010100100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 r0 r1 r2 r3 r4 r5 r6 r7 r8
+  have hstep := r9.1
+  have hparity := r9.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `0101001001`. -/
+theorem parameters_0101001001
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    : ∃ q : Nat, x0 = 128*q+86 ∧ x1 = 64*q+43 ∧ x2 = 192*q+130 ∧ x3 = 96*q+65 ∧ x4 = 288*q+196 ∧ x5 = 144*q+98 ∧ x6 = 72*q+49 ∧ x7 = 216*q+148 ∧ x8 = 108*q+74 ∧ x9 = 54*q+37 ∧ x10 = 162*q+112 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9⟩ := parameters_010100100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 r0 r1 r2 r3 r4 r5 r6 r7 r8
+  have hstep := r9.1
+  have hparity := r9.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `0101001010`. -/
+theorem parameters_0101001010
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    : ∃ q : Nat, x0 = 64*q+54 ∧ x1 = 32*q+27 ∧ x2 = 96*q+82 ∧ x3 = 48*q+41 ∧ x4 = 144*q+124 ∧ x5 = 72*q+62 ∧ x6 = 36*q+31 ∧ x7 = 108*q+94 ∧ x8 = 54*q+47 ∧ x9 = 162*q+142 ∧ x10 = 81*q+71 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9⟩ := parameters_010100101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 r0 r1 r2 r3 r4 r5 r6 r7 r8
+  have hstep := r9.1
+  have hparity := r9.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  clear hparity
+  refine ⟨q,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `1001010010`. -/
+theorem parameters_1001010010
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    : ∃ q : Nat, x0 = 64*q+57 ∧ x1 = 192*q+172 ∧ x2 = 96*q+86 ∧ x3 = 48*q+43 ∧ x4 = 144*q+130 ∧ x5 = 72*q+65 ∧ x6 = 216*q+196 ∧ x7 = 108*q+98 ∧ x8 = 54*q+49 ∧ x9 = 162*q+148 ∧ x10 = 81*q+74 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9⟩ := parameters_100101001 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 r0 r1 r2 r3 r4 r5 r6 r7 r8
+  have hstep := r9.1
+  have hparity := r9.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  clear hparity
+  refine ⟨q,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `1010010100`. -/
+theorem parameters_1010010100
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    : ∃ q : Nat, x0 = 64*q+59 ∧ x1 = 192*q+178 ∧ x2 = 96*q+89 ∧ x3 = 288*q+268 ∧ x4 = 144*q+134 ∧ x5 = 72*q+67 ∧ x6 = 216*q+202 ∧ x7 = 108*q+101 ∧ x8 = 324*q+304 ∧ x9 = 162*q+152 ∧ x10 = 81*q+76 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9⟩ := parameters_101001010 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 r0 r1 r2 r3 r4 r5 r6 r7 r8
+  have hstep := r9.1
+  have hparity := r9.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `1010010101`. -/
+theorem parameters_1010010101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    : ∃ q : Nat, x0 = 64*q+27 ∧ x1 = 192*q+82 ∧ x2 = 96*q+41 ∧ x3 = 288*q+124 ∧ x4 = 144*q+62 ∧ x5 = 72*q+31 ∧ x6 = 216*q+94 ∧ x7 = 108*q+47 ∧ x8 = 324*q+142 ∧ x9 = 162*q+71 ∧ x10 = 486*q+214 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9⟩ := parameters_101001010 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 r0 r1 r2 r3 r4 r5 r6 r7 r8
+  have hstep := r9.1
+  have hparity := r9.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `00101001000`. -/
+theorem parameters_00101001000
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    : ∃ q : Nat, x0 = 256*q+44 ∧ x1 = 128*q+22 ∧ x2 = 64*q+11 ∧ x3 = 192*q+34 ∧ x4 = 96*q+17 ∧ x5 = 288*q+52 ∧ x6 = 144*q+26 ∧ x7 = 72*q+13 ∧ x8 = 216*q+40 ∧ x9 = 108*q+20 ∧ x10 = 54*q+10 ∧ x11 = 27*q+5 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10⟩ := parameters_0010100100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  have hstep := r10.1
+  have hparity := r10.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `00101001001`. -/
+theorem parameters_00101001001
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (x11 = 3*x10+1 ∧ x10%2 = 1))
+    : ∃ q : Nat, x0 = 256*q+172 ∧ x1 = 128*q+86 ∧ x2 = 64*q+43 ∧ x3 = 192*q+130 ∧ x4 = 96*q+65 ∧ x5 = 288*q+196 ∧ x6 = 144*q+98 ∧ x7 = 72*q+49 ∧ x8 = 216*q+148 ∧ x9 = 108*q+74 ∧ x10 = 54*q+37 ∧ x11 = 162*q+112 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10⟩ := parameters_0010100100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  have hstep := r10.1
+  have hparity := r10.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `00101001010`. -/
+theorem parameters_00101001010
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    : ∃ q : Nat, x0 = 128*q+108 ∧ x1 = 64*q+54 ∧ x2 = 32*q+27 ∧ x3 = 96*q+82 ∧ x4 = 48*q+41 ∧ x5 = 144*q+124 ∧ x6 = 72*q+62 ∧ x7 = 36*q+31 ∧ x8 = 108*q+94 ∧ x9 = 54*q+47 ∧ x10 = 162*q+142 ∧ x11 = 81*q+71 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10⟩ := parameters_0010100101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  have hstep := r10.1
+  have hparity := r10.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  clear hparity
+  refine ⟨q,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `01001010010`. -/
+theorem parameters_01001010010
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    : ∃ q : Nat, x0 = 128*q+114 ∧ x1 = 64*q+57 ∧ x2 = 192*q+172 ∧ x3 = 96*q+86 ∧ x4 = 48*q+43 ∧ x5 = 144*q+130 ∧ x6 = 72*q+65 ∧ x7 = 216*q+196 ∧ x8 = 108*q+98 ∧ x9 = 54*q+49 ∧ x10 = 162*q+148 ∧ x11 = 81*q+74 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10⟩ := parameters_0100101001 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  have hstep := r10.1
+  have hparity := r10.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  clear hparity
+  refine ⟨q,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `01010010100`. -/
+theorem parameters_01010010100
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    : ∃ q : Nat, x0 = 128*q+118 ∧ x1 = 64*q+59 ∧ x2 = 192*q+178 ∧ x3 = 96*q+89 ∧ x4 = 288*q+268 ∧ x5 = 144*q+134 ∧ x6 = 72*q+67 ∧ x7 = 216*q+202 ∧ x8 = 108*q+101 ∧ x9 = 324*q+304 ∧ x10 = 162*q+152 ∧ x11 = 81*q+76 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10⟩ := parameters_0101001010 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  have hstep := r10.1
+  have hparity := r10.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `01010010101`. -/
+theorem parameters_01010010101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (x11 = 3*x10+1 ∧ x10%2 = 1))
+    : ∃ q : Nat, x0 = 128*q+54 ∧ x1 = 64*q+27 ∧ x2 = 192*q+82 ∧ x3 = 96*q+41 ∧ x4 = 288*q+124 ∧ x5 = 144*q+62 ∧ x6 = 72*q+31 ∧ x7 = 216*q+94 ∧ x8 = 108*q+47 ∧ x9 = 324*q+142 ∧ x10 = 162*q+71 ∧ x11 = 486*q+214 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10⟩ := parameters_0101001010 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  have hstep := r10.1
+  have hparity := r10.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `10010100100`. -/
+theorem parameters_10010100100
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    : ∃ q : Nat, x0 = 128*q+57 ∧ x1 = 384*q+172 ∧ x2 = 192*q+86 ∧ x3 = 96*q+43 ∧ x4 = 288*q+130 ∧ x5 = 144*q+65 ∧ x6 = 432*q+196 ∧ x7 = 216*q+98 ∧ x8 = 108*q+49 ∧ x9 = 324*q+148 ∧ x10 = 162*q+74 ∧ x11 = 81*q+37 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10⟩ := parameters_1001010010 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  have hstep := r10.1
+  have hparity := r10.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `10010100101`. -/
+theorem parameters_10010100101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (x11 = 3*x10+1 ∧ x10%2 = 1))
+    : ∃ q : Nat, x0 = 128*q+121 ∧ x1 = 384*q+364 ∧ x2 = 192*q+182 ∧ x3 = 96*q+91 ∧ x4 = 288*q+274 ∧ x5 = 144*q+137 ∧ x6 = 432*q+412 ∧ x7 = 216*q+206 ∧ x8 = 108*q+103 ∧ x9 = 324*q+310 ∧ x10 = 162*q+155 ∧ x11 = 486*q+466 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10⟩ := parameters_1001010010 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  have hstep := r10.1
+  have hparity := r10.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `10100101000`. -/
+theorem parameters_10100101000
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    : ∃ q : Nat, x0 = 128*q+59 ∧ x1 = 384*q+178 ∧ x2 = 192*q+89 ∧ x3 = 576*q+268 ∧ x4 = 288*q+134 ∧ x5 = 144*q+67 ∧ x6 = 432*q+202 ∧ x7 = 216*q+101 ∧ x8 = 648*q+304 ∧ x9 = 324*q+152 ∧ x10 = 162*q+76 ∧ x11 = 81*q+38 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10⟩ := parameters_1010010100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  have hstep := r10.1
+  have hparity := r10.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `10100101001`. -/
+theorem parameters_10100101001
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (x11 = 3*x10+1 ∧ x10%2 = 1))
+    : ∃ q : Nat, x0 = 128*q+123 ∧ x1 = 384*q+370 ∧ x2 = 192*q+185 ∧ x3 = 576*q+556 ∧ x4 = 288*q+278 ∧ x5 = 144*q+139 ∧ x6 = 432*q+418 ∧ x7 = 216*q+209 ∧ x8 = 648*q+628 ∧ x9 = 324*q+314 ∧ x10 = 162*q+157 ∧ x11 = 486*q+472 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10⟩ := parameters_1010010100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  have hstep := r10.1
+  have hparity := r10.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `001010010100`. -/
+theorem parameters_001010010100
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    : ∃ q : Nat, x0 = 256*q+236 ∧ x1 = 128*q+118 ∧ x2 = 64*q+59 ∧ x3 = 192*q+178 ∧ x4 = 96*q+89 ∧ x5 = 288*q+268 ∧ x6 = 144*q+134 ∧ x7 = 72*q+67 ∧ x8 = 216*q+202 ∧ x9 = 108*q+101 ∧ x10 = 324*q+304 ∧ x11 = 162*q+152 ∧ x12 = 81*q+76 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11⟩ := parameters_00101001010 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  have hstep := r11.1
+  have hparity := r11.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `001010010101`. -/
+theorem parameters_001010010101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (x12 = 3*x11+1 ∧ x11%2 = 1))
+    : ∃ q : Nat, x0 = 256*q+108 ∧ x1 = 128*q+54 ∧ x2 = 64*q+27 ∧ x3 = 192*q+82 ∧ x4 = 96*q+41 ∧ x5 = 288*q+124 ∧ x6 = 144*q+62 ∧ x7 = 72*q+31 ∧ x8 = 216*q+94 ∧ x9 = 108*q+47 ∧ x10 = 324*q+142 ∧ x11 = 162*q+71 ∧ x12 = 486*q+214 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11⟩ := parameters_00101001010 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  have hstep := r11.1
+  have hparity := r11.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `010010100100`. -/
+theorem parameters_010010100100
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    : ∃ q : Nat, x0 = 256*q+114 ∧ x1 = 128*q+57 ∧ x2 = 384*q+172 ∧ x3 = 192*q+86 ∧ x4 = 96*q+43 ∧ x5 = 288*q+130 ∧ x6 = 144*q+65 ∧ x7 = 432*q+196 ∧ x8 = 216*q+98 ∧ x9 = 108*q+49 ∧ x10 = 324*q+148 ∧ x11 = 162*q+74 ∧ x12 = 81*q+37 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11⟩ := parameters_01001010010 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  have hstep := r11.1
+  have hparity := r11.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `010010100101`. -/
+theorem parameters_010010100101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (x12 = 3*x11+1 ∧ x11%2 = 1))
+    : ∃ q : Nat, x0 = 256*q+242 ∧ x1 = 128*q+121 ∧ x2 = 384*q+364 ∧ x3 = 192*q+182 ∧ x4 = 96*q+91 ∧ x5 = 288*q+274 ∧ x6 = 144*q+137 ∧ x7 = 432*q+412 ∧ x8 = 216*q+206 ∧ x9 = 108*q+103 ∧ x10 = 324*q+310 ∧ x11 = 162*q+155 ∧ x12 = 486*q+466 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11⟩ := parameters_01001010010 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  have hstep := r11.1
+  have hparity := r11.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `010100101000`. -/
+theorem parameters_010100101000
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    : ∃ q : Nat, x0 = 256*q+118 ∧ x1 = 128*q+59 ∧ x2 = 384*q+178 ∧ x3 = 192*q+89 ∧ x4 = 576*q+268 ∧ x5 = 288*q+134 ∧ x6 = 144*q+67 ∧ x7 = 432*q+202 ∧ x8 = 216*q+101 ∧ x9 = 648*q+304 ∧ x10 = 324*q+152 ∧ x11 = 162*q+76 ∧ x12 = 81*q+38 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11⟩ := parameters_01010010100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  have hstep := r11.1
+  have hparity := r11.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `010100101001`. -/
+theorem parameters_010100101001
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (x12 = 3*x11+1 ∧ x11%2 = 1))
+    : ∃ q : Nat, x0 = 256*q+246 ∧ x1 = 128*q+123 ∧ x2 = 384*q+370 ∧ x3 = 192*q+185 ∧ x4 = 576*q+556 ∧ x5 = 288*q+278 ∧ x6 = 144*q+139 ∧ x7 = 432*q+418 ∧ x8 = 216*q+209 ∧ x9 = 648*q+628 ∧ x10 = 324*q+314 ∧ x11 = 162*q+157 ∧ x12 = 486*q+472 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11⟩ := parameters_01010010100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  have hstep := r11.1
+  have hparity := r11.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `100101001010`. -/
+theorem parameters_100101001010
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (x11 = 3*x10+1 ∧ x10%2 = 1))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    : ∃ q : Nat, x0 = 128*q+121 ∧ x1 = 384*q+364 ∧ x2 = 192*q+182 ∧ x3 = 96*q+91 ∧ x4 = 288*q+274 ∧ x5 = 144*q+137 ∧ x6 = 432*q+412 ∧ x7 = 216*q+206 ∧ x8 = 108*q+103 ∧ x9 = 324*q+310 ∧ x10 = 162*q+155 ∧ x11 = 486*q+466 ∧ x12 = 243*q+233 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11⟩ := parameters_10010100101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  have hstep := r11.1
+  have hparity := r11.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11
+  clear hparity
+  refine ⟨q,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `101001010010`. -/
+theorem parameters_101001010010
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (x11 = 3*x10+1 ∧ x10%2 = 1))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    : ∃ q : Nat, x0 = 128*q+123 ∧ x1 = 384*q+370 ∧ x2 = 192*q+185 ∧ x3 = 576*q+556 ∧ x4 = 288*q+278 ∧ x5 = 144*q+139 ∧ x6 = 432*q+418 ∧ x7 = 216*q+209 ∧ x8 = 648*q+628 ∧ x9 = 324*q+314 ∧ x10 = 162*q+157 ∧ x11 = 486*q+472 ∧ x12 = 243*q+236 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11⟩ := parameters_10100101001 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  have hstep := r11.1
+  have hparity := r11.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11
+  clear hparity
+  refine ⟨q,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `0010100101000`. -/
+theorem parameters_0010100101000
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    : ∃ q : Nat, x0 = 512*q+236 ∧ x1 = 256*q+118 ∧ x2 = 128*q+59 ∧ x3 = 384*q+178 ∧ x4 = 192*q+89 ∧ x5 = 576*q+268 ∧ x6 = 288*q+134 ∧ x7 = 144*q+67 ∧ x8 = 432*q+202 ∧ x9 = 216*q+101 ∧ x10 = 648*q+304 ∧ x11 = 324*q+152 ∧ x12 = 162*q+76 ∧ x13 = 81*q+38 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12⟩ := parameters_001010010100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11
+  have hstep := r12.1
+  have hparity := r12.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `0010100101001`. -/
+theorem parameters_0010100101001
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    (r12 : (x13 = 3*x12+1 ∧ x12%2 = 1))
+    : ∃ q : Nat, x0 = 512*q+492 ∧ x1 = 256*q+246 ∧ x2 = 128*q+123 ∧ x3 = 384*q+370 ∧ x4 = 192*q+185 ∧ x5 = 576*q+556 ∧ x6 = 288*q+278 ∧ x7 = 144*q+139 ∧ x8 = 432*q+418 ∧ x9 = 216*q+209 ∧ x10 = 648*q+628 ∧ x11 = 324*q+314 ∧ x12 = 162*q+157 ∧ x13 = 486*q+472 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12⟩ := parameters_001010010100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11
+  have hstep := r12.1
+  have hparity := r12.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `0100101001010`. -/
+theorem parameters_0100101001010
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (x12 = 3*x11+1 ∧ x11%2 = 1))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    : ∃ q : Nat, x0 = 256*q+242 ∧ x1 = 128*q+121 ∧ x2 = 384*q+364 ∧ x3 = 192*q+182 ∧ x4 = 96*q+91 ∧ x5 = 288*q+274 ∧ x6 = 144*q+137 ∧ x7 = 432*q+412 ∧ x8 = 216*q+206 ∧ x9 = 108*q+103 ∧ x10 = 324*q+310 ∧ x11 = 162*q+155 ∧ x12 = 486*q+466 ∧ x13 = 243*q+233 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12⟩ := parameters_010010100101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11
+  have hstep := r12.1
+  have hparity := r12.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12
+  clear hparity
+  refine ⟨q,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `0101001010010`. -/
+theorem parameters_0101001010010
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (x12 = 3*x11+1 ∧ x11%2 = 1))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    : ∃ q : Nat, x0 = 256*q+246 ∧ x1 = 128*q+123 ∧ x2 = 384*q+370 ∧ x3 = 192*q+185 ∧ x4 = 576*q+556 ∧ x5 = 288*q+278 ∧ x6 = 144*q+139 ∧ x7 = 432*q+418 ∧ x8 = 216*q+209 ∧ x9 = 648*q+628 ∧ x10 = 324*q+314 ∧ x11 = 162*q+157 ∧ x12 = 486*q+472 ∧ x13 = 243*q+236 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12⟩ := parameters_010100101001 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11
+  have hstep := r12.1
+  have hparity := r12.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12
+  clear hparity
+  refine ⟨q,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `1001010010100`. -/
+theorem parameters_1001010010100
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (x11 = 3*x10+1 ∧ x10%2 = 1))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    : ∃ q : Nat, x0 = 256*q+249 ∧ x1 = 768*q+748 ∧ x2 = 384*q+374 ∧ x3 = 192*q+187 ∧ x4 = 576*q+562 ∧ x5 = 288*q+281 ∧ x6 = 864*q+844 ∧ x7 = 432*q+422 ∧ x8 = 216*q+211 ∧ x9 = 648*q+634 ∧ x10 = 324*q+317 ∧ x11 = 972*q+952 ∧ x12 = 486*q+476 ∧ x13 = 243*q+238 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12⟩ := parameters_100101001010 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11
+  have hstep := r12.1
+  have hparity := r12.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `1001010010101`. -/
+theorem parameters_1001010010101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (x11 = 3*x10+1 ∧ x10%2 = 1))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    (r12 : (x13 = 3*x12+1 ∧ x12%2 = 1))
+    : ∃ q : Nat, x0 = 256*q+121 ∧ x1 = 768*q+364 ∧ x2 = 384*q+182 ∧ x3 = 192*q+91 ∧ x4 = 576*q+274 ∧ x5 = 288*q+137 ∧ x6 = 864*q+412 ∧ x7 = 432*q+206 ∧ x8 = 216*q+103 ∧ x9 = 648*q+310 ∧ x10 = 324*q+155 ∧ x11 = 972*q+466 ∧ x12 = 486*q+233 ∧ x13 = 1458*q+700 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12⟩ := parameters_100101001010 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11
+  have hstep := r12.1
+  have hparity := r12.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `1010010100100`. -/
+theorem parameters_1010010100100
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (x11 = 3*x10+1 ∧ x10%2 = 1))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    : ∃ q : Nat, x0 = 256*q+123 ∧ x1 = 768*q+370 ∧ x2 = 384*q+185 ∧ x3 = 1152*q+556 ∧ x4 = 576*q+278 ∧ x5 = 288*q+139 ∧ x6 = 864*q+418 ∧ x7 = 432*q+209 ∧ x8 = 1296*q+628 ∧ x9 = 648*q+314 ∧ x10 = 324*q+157 ∧ x11 = 972*q+472 ∧ x12 = 486*q+236 ∧ x13 = 243*q+118 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12⟩ := parameters_101001010010 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11
+  have hstep := r12.1
+  have hparity := r12.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `1010010100101`. -/
+theorem parameters_1010010100101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (x11 = 3*x10+1 ∧ x10%2 = 1))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    (r12 : (x13 = 3*x12+1 ∧ x12%2 = 1))
+    : ∃ q : Nat, x0 = 256*q+251 ∧ x1 = 768*q+754 ∧ x2 = 384*q+377 ∧ x3 = 1152*q+1132 ∧ x4 = 576*q+566 ∧ x5 = 288*q+283 ∧ x6 = 864*q+850 ∧ x7 = 432*q+425 ∧ x8 = 1296*q+1276 ∧ x9 = 648*q+638 ∧ x10 = 324*q+319 ∧ x11 = 972*q+958 ∧ x12 = 486*q+479 ∧ x13 = 1458*q+1438 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12⟩ := parameters_101001010010 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11
+  have hstep := r12.1
+  have hparity := r12.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `00101001010010`. -/
+theorem parameters_00101001010010
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    (r12 : (x13 = 3*x12+1 ∧ x12%2 = 1))
+    (r13 : (2*x14 = x13 ∧ x13%2 = 0))
+    : ∃ q : Nat, x0 = 512*q+492 ∧ x1 = 256*q+246 ∧ x2 = 128*q+123 ∧ x3 = 384*q+370 ∧ x4 = 192*q+185 ∧ x5 = 576*q+556 ∧ x6 = 288*q+278 ∧ x7 = 144*q+139 ∧ x8 = 432*q+418 ∧ x9 = 216*q+209 ∧ x10 = 648*q+628 ∧ x11 = 324*q+314 ∧ x12 = 162*q+157 ∧ x13 = 486*q+472 ∧ x14 = 243*q+236 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13⟩ := parameters_0010100101001 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12
+  have hstep := r13.1
+  have hparity := r13.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13
+  clear hparity
+  refine ⟨q,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `01001010010100`. -/
+theorem parameters_01001010010100
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (x12 = 3*x11+1 ∧ x11%2 = 1))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    (r13 : (2*x14 = x13 ∧ x13%2 = 0))
+    : ∃ q : Nat, x0 = 512*q+498 ∧ x1 = 256*q+249 ∧ x2 = 768*q+748 ∧ x3 = 384*q+374 ∧ x4 = 192*q+187 ∧ x5 = 576*q+562 ∧ x6 = 288*q+281 ∧ x7 = 864*q+844 ∧ x8 = 432*q+422 ∧ x9 = 216*q+211 ∧ x10 = 648*q+634 ∧ x11 = 324*q+317 ∧ x12 = 972*q+952 ∧ x13 = 486*q+476 ∧ x14 = 243*q+238 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13⟩ := parameters_0100101001010 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12
+  have hstep := r13.1
+  have hparity := r13.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `01001010010101`. -/
+theorem parameters_01001010010101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (x12 = 3*x11+1 ∧ x11%2 = 1))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    (r13 : (x14 = 3*x13+1 ∧ x13%2 = 1))
+    : ∃ q : Nat, x0 = 512*q+242 ∧ x1 = 256*q+121 ∧ x2 = 768*q+364 ∧ x3 = 384*q+182 ∧ x4 = 192*q+91 ∧ x5 = 576*q+274 ∧ x6 = 288*q+137 ∧ x7 = 864*q+412 ∧ x8 = 432*q+206 ∧ x9 = 216*q+103 ∧ x10 = 648*q+310 ∧ x11 = 324*q+155 ∧ x12 = 972*q+466 ∧ x13 = 486*q+233 ∧ x14 = 1458*q+700 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13⟩ := parameters_0100101001010 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12
+  have hstep := r13.1
+  have hparity := r13.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `01010010100100`. -/
+theorem parameters_01010010100100
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (x12 = 3*x11+1 ∧ x11%2 = 1))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    (r13 : (2*x14 = x13 ∧ x13%2 = 0))
+    : ∃ q : Nat, x0 = 512*q+246 ∧ x1 = 256*q+123 ∧ x2 = 768*q+370 ∧ x3 = 384*q+185 ∧ x4 = 1152*q+556 ∧ x5 = 576*q+278 ∧ x6 = 288*q+139 ∧ x7 = 864*q+418 ∧ x8 = 432*q+209 ∧ x9 = 1296*q+628 ∧ x10 = 648*q+314 ∧ x11 = 324*q+157 ∧ x12 = 972*q+472 ∧ x13 = 486*q+236 ∧ x14 = 243*q+118 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13⟩ := parameters_0101001010010 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12
+  have hstep := r13.1
+  have hparity := r13.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `01010010100101`. -/
+theorem parameters_01010010100101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (x12 = 3*x11+1 ∧ x11%2 = 1))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    (r13 : (x14 = 3*x13+1 ∧ x13%2 = 1))
+    : ∃ q : Nat, x0 = 512*q+502 ∧ x1 = 256*q+251 ∧ x2 = 768*q+754 ∧ x3 = 384*q+377 ∧ x4 = 1152*q+1132 ∧ x5 = 576*q+566 ∧ x6 = 288*q+283 ∧ x7 = 864*q+850 ∧ x8 = 432*q+425 ∧ x9 = 1296*q+1276 ∧ x10 = 648*q+638 ∧ x11 = 324*q+319 ∧ x12 = 972*q+958 ∧ x13 = 486*q+479 ∧ x14 = 1458*q+1438 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13⟩ := parameters_0101001010010 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12
+  have hstep := r13.1
+  have hparity := r13.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `10010100101000`. -/
+theorem parameters_10010100101000
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (x11 = 3*x10+1 ∧ x10%2 = 1))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    (r13 : (2*x14 = x13 ∧ x13%2 = 0))
+    : ∃ q : Nat, x0 = 512*q+249 ∧ x1 = 1536*q+748 ∧ x2 = 768*q+374 ∧ x3 = 384*q+187 ∧ x4 = 1152*q+562 ∧ x5 = 576*q+281 ∧ x6 = 1728*q+844 ∧ x7 = 864*q+422 ∧ x8 = 432*q+211 ∧ x9 = 1296*q+634 ∧ x10 = 648*q+317 ∧ x11 = 1944*q+952 ∧ x12 = 972*q+476 ∧ x13 = 486*q+238 ∧ x14 = 243*q+119 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13⟩ := parameters_1001010010100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12
+  have hstep := r13.1
+  have hparity := r13.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `10010100101001`. -/
+theorem parameters_10010100101001
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (x11 = 3*x10+1 ∧ x10%2 = 1))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    (r13 : (x14 = 3*x13+1 ∧ x13%2 = 1))
+    : ∃ q : Nat, x0 = 512*q+505 ∧ x1 = 1536*q+1516 ∧ x2 = 768*q+758 ∧ x3 = 384*q+379 ∧ x4 = 1152*q+1138 ∧ x5 = 576*q+569 ∧ x6 = 1728*q+1708 ∧ x7 = 864*q+854 ∧ x8 = 432*q+427 ∧ x9 = 1296*q+1282 ∧ x10 = 648*q+641 ∧ x11 = 1944*q+1924 ∧ x12 = 972*q+962 ∧ x13 = 486*q+481 ∧ x14 = 1458*q+1444 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13⟩ := parameters_1001010010100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12
+  have hstep := r13.1
+  have hparity := r13.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `001010010100100`. -/
+theorem parameters_001010010100100
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    (r12 : (x13 = 3*x12+1 ∧ x12%2 = 1))
+    (r13 : (2*x14 = x13 ∧ x13%2 = 0))
+    (r14 : (2*x15 = x14 ∧ x14%2 = 0))
+    : ∃ q : Nat, x0 = 1024*q+492 ∧ x1 = 512*q+246 ∧ x2 = 256*q+123 ∧ x3 = 768*q+370 ∧ x4 = 384*q+185 ∧ x5 = 1152*q+556 ∧ x6 = 576*q+278 ∧ x7 = 288*q+139 ∧ x8 = 864*q+418 ∧ x9 = 432*q+209 ∧ x10 = 1296*q+628 ∧ x11 = 648*q+314 ∧ x12 = 324*q+157 ∧ x13 = 972*q+472 ∧ x14 = 486*q+236 ∧ x15 = 243*q+118 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14⟩ := parameters_00101001010010 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13
+  have hstep := r14.1
+  have hparity := r14.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `001010010100101`. -/
+theorem parameters_001010010100101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    (r12 : (x13 = 3*x12+1 ∧ x12%2 = 1))
+    (r13 : (2*x14 = x13 ∧ x13%2 = 0))
+    (r14 : (x15 = 3*x14+1 ∧ x14%2 = 1))
+    : ∃ q : Nat, x0 = 1024*q+1004 ∧ x1 = 512*q+502 ∧ x2 = 256*q+251 ∧ x3 = 768*q+754 ∧ x4 = 384*q+377 ∧ x5 = 1152*q+1132 ∧ x6 = 576*q+566 ∧ x7 = 288*q+283 ∧ x8 = 864*q+850 ∧ x9 = 432*q+425 ∧ x10 = 1296*q+1276 ∧ x11 = 648*q+638 ∧ x12 = 324*q+319 ∧ x13 = 972*q+958 ∧ x14 = 486*q+479 ∧ x15 = 1458*q+1438 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14⟩ := parameters_00101001010010 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13
+  have hstep := r14.1
+  have hparity := r14.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `010010100101000`. -/
+theorem parameters_010010100101000
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (x12 = 3*x11+1 ∧ x11%2 = 1))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    (r13 : (2*x14 = x13 ∧ x13%2 = 0))
+    (r14 : (2*x15 = x14 ∧ x14%2 = 0))
+    : ∃ q : Nat, x0 = 1024*q+498 ∧ x1 = 512*q+249 ∧ x2 = 1536*q+748 ∧ x3 = 768*q+374 ∧ x4 = 384*q+187 ∧ x5 = 1152*q+562 ∧ x6 = 576*q+281 ∧ x7 = 1728*q+844 ∧ x8 = 864*q+422 ∧ x9 = 432*q+211 ∧ x10 = 1296*q+634 ∧ x11 = 648*q+317 ∧ x12 = 1944*q+952 ∧ x13 = 972*q+476 ∧ x14 = 486*q+238 ∧ x15 = 243*q+119 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14⟩ := parameters_01001010010100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13
+  have hstep := r14.1
+  have hparity := r14.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `010010100101001`. -/
+theorem parameters_010010100101001
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (x12 = 3*x11+1 ∧ x11%2 = 1))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    (r13 : (2*x14 = x13 ∧ x13%2 = 0))
+    (r14 : (x15 = 3*x14+1 ∧ x14%2 = 1))
+    : ∃ q : Nat, x0 = 1024*q+1010 ∧ x1 = 512*q+505 ∧ x2 = 1536*q+1516 ∧ x3 = 768*q+758 ∧ x4 = 384*q+379 ∧ x5 = 1152*q+1138 ∧ x6 = 576*q+569 ∧ x7 = 1728*q+1708 ∧ x8 = 864*q+854 ∧ x9 = 432*q+427 ∧ x10 = 1296*q+1282 ∧ x11 = 648*q+641 ∧ x12 = 1944*q+1924 ∧ x13 = 972*q+962 ∧ x14 = 486*q+481 ∧ x15 = 1458*q+1444 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14⟩ := parameters_01001010010100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13
+  have hstep := r14.1
+  have hparity := r14.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `100101001010010`. -/
+theorem parameters_100101001010010
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (x11 = 3*x10+1 ∧ x10%2 = 1))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    (r13 : (x14 = 3*x13+1 ∧ x13%2 = 1))
+    (r14 : (2*x15 = x14 ∧ x14%2 = 0))
+    : ∃ q : Nat, x0 = 512*q+505 ∧ x1 = 1536*q+1516 ∧ x2 = 768*q+758 ∧ x3 = 384*q+379 ∧ x4 = 1152*q+1138 ∧ x5 = 576*q+569 ∧ x6 = 1728*q+1708 ∧ x7 = 864*q+854 ∧ x8 = 432*q+427 ∧ x9 = 1296*q+1282 ∧ x10 = 648*q+641 ∧ x11 = 1944*q+1924 ∧ x12 = 972*q+962 ∧ x13 = 486*q+481 ∧ x14 = 1458*q+1444 ∧ x15 = 729*q+722 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14⟩ := parameters_10010100101001 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13
+  have hstep := r14.1
+  have hparity := r14.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14
+  clear hparity
+  refine ⟨q,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `0100101001010010`. -/
+theorem parameters_0100101001010010
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (x12 = 3*x11+1 ∧ x11%2 = 1))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    (r13 : (2*x14 = x13 ∧ x13%2 = 0))
+    (r14 : (x15 = 3*x14+1 ∧ x14%2 = 1))
+    (r15 : (2*x16 = x15 ∧ x15%2 = 0))
+    : ∃ q : Nat, x0 = 1024*q+1010 ∧ x1 = 512*q+505 ∧ x2 = 1536*q+1516 ∧ x3 = 768*q+758 ∧ x4 = 384*q+379 ∧ x5 = 1152*q+1138 ∧ x6 = 576*q+569 ∧ x7 = 1728*q+1708 ∧ x8 = 864*q+854 ∧ x9 = 432*q+427 ∧ x10 = 1296*q+1282 ∧ x11 = 648*q+641 ∧ x12 = 1944*q+1924 ∧ x13 = 972*q+962 ∧ x14 = 486*q+481 ∧ x15 = 1458*q+1444 ∧ x16 = 729*q+722 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15⟩ := parameters_010010100101001 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14
+  have hstep := r15.1
+  have hparity := r15.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14 r15
+  clear hparity
+  refine ⟨q,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `1001010010100100`. -/
+theorem parameters_1001010010100100
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (x11 = 3*x10+1 ∧ x10%2 = 1))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    (r13 : (x14 = 3*x13+1 ∧ x13%2 = 1))
+    (r14 : (2*x15 = x14 ∧ x14%2 = 0))
+    (r15 : (2*x16 = x15 ∧ x15%2 = 0))
+    : ∃ q : Nat, x0 = 1024*q+505 ∧ x1 = 3072*q+1516 ∧ x2 = 1536*q+758 ∧ x3 = 768*q+379 ∧ x4 = 2304*q+1138 ∧ x5 = 1152*q+569 ∧ x6 = 3456*q+1708 ∧ x7 = 1728*q+854 ∧ x8 = 864*q+427 ∧ x9 = 2592*q+1282 ∧ x10 = 1296*q+641 ∧ x11 = 3888*q+1924 ∧ x12 = 1944*q+962 ∧ x13 = 972*q+481 ∧ x14 = 2916*q+1444 ∧ x15 = 1458*q+722 ∧ x16 = 729*q+361 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15⟩ := parameters_100101001010010 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14
+  have hstep := r15.1
+  have hparity := r15.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14 r15
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `1001010010100101`. -/
+theorem parameters_1001010010100101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 : Nat)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (x11 = 3*x10+1 ∧ x10%2 = 1))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    (r13 : (x14 = 3*x13+1 ∧ x13%2 = 1))
+    (r14 : (2*x15 = x14 ∧ x14%2 = 0))
+    (r15 : (x16 = 3*x15+1 ∧ x15%2 = 1))
+    : ∃ q : Nat, x0 = 1024*q+1017 ∧ x1 = 3072*q+3052 ∧ x2 = 1536*q+1526 ∧ x3 = 768*q+763 ∧ x4 = 2304*q+2290 ∧ x5 = 1152*q+1145 ∧ x6 = 3456*q+3436 ∧ x7 = 1728*q+1718 ∧ x8 = 864*q+859 ∧ x9 = 2592*q+2578 ∧ x10 = 1296*q+1289 ∧ x11 = 3888*q+3868 ∧ x12 = 1944*q+1934 ∧ x13 = 972*q+967 ∧ x14 = 2916*q+2902 ∧ x15 = 1458*q+1451 ∧ x16 = 4374*q+4354 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15⟩ := parameters_100101001010010 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14
+  have hstep := r15.1
+  have hparity := r15.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14 r15
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `01001010010100100`. -/
+theorem parameters_01001010010100100
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (x12 = 3*x11+1 ∧ x11%2 = 1))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    (r13 : (2*x14 = x13 ∧ x13%2 = 0))
+    (r14 : (x15 = 3*x14+1 ∧ x14%2 = 1))
+    (r15 : (2*x16 = x15 ∧ x15%2 = 0))
+    (r16 : (2*x17 = x16 ∧ x16%2 = 0))
+    : ∃ q : Nat, x0 = 2048*q+1010 ∧ x1 = 1024*q+505 ∧ x2 = 3072*q+1516 ∧ x3 = 1536*q+758 ∧ x4 = 768*q+379 ∧ x5 = 2304*q+1138 ∧ x6 = 1152*q+569 ∧ x7 = 3456*q+1708 ∧ x8 = 1728*q+854 ∧ x9 = 864*q+427 ∧ x10 = 2592*q+1282 ∧ x11 = 1296*q+641 ∧ x12 = 3888*q+1924 ∧ x13 = 1944*q+962 ∧ x14 = 972*q+481 ∧ x15 = 2916*q+1444 ∧ x16 = 1458*q+722 ∧ x17 = 729*q+361 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16⟩ := parameters_0100101001010010 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14 r15
+  have hstep := r16.1
+  have hparity := r16.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14 r15 r16
+  have hq : q = 2*(q/2)+0 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Exact source residue and full affine trace for branch `01001010010100101`. -/
+theorem parameters_01001010010100101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 : Nat)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (x12 = 3*x11+1 ∧ x11%2 = 1))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    (r13 : (2*x14 = x13 ∧ x13%2 = 0))
+    (r14 : (x15 = 3*x14+1 ∧ x14%2 = 1))
+    (r15 : (2*x16 = x15 ∧ x15%2 = 0))
+    (r16 : (x17 = 3*x16+1 ∧ x16%2 = 1))
+    : ∃ q : Nat, x0 = 2048*q+2034 ∧ x1 = 1024*q+1017 ∧ x2 = 3072*q+3052 ∧ x3 = 1536*q+1526 ∧ x4 = 768*q+763 ∧ x5 = 2304*q+2290 ∧ x6 = 1152*q+1145 ∧ x7 = 3456*q+3436 ∧ x8 = 1728*q+1718 ∧ x9 = 864*q+859 ∧ x10 = 2592*q+2578 ∧ x11 = 1296*q+1289 ∧ x12 = 3888*q+3868 ∧ x13 = 1944*q+1934 ∧ x14 = 972*q+967 ∧ x15 = 2916*q+2902 ∧ x16 = 1458*q+1451 ∧ x17 = 4374*q+4354 := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16⟩ := parameters_0100101001010010 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14 r15
+  have hstep := r16.1
+  have hparity := r16.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14 r15 r16
+  have hq : q = 2*(q/2)+1 := by omega
+  clear hparity
+  refine ⟨q/2,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_,?_⟩ <;> omega
+
+/-- Terminal branch `000` cannot satisfy the band bounds. -/
+theorem exclude_000
+    (x0 x1 x2 x3 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h0 : b ≤ x0 ∧ 4*x0 ≤ 21*b)
+    (h3 : b ≤ x3 ∧ 4*x3 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3⟩ := parameters_000 x0 x1 x2 x3 r0 r1 r2
+  clear r0 r1 r2
+  omega
+
+/-- Terminal branch `001000` cannot satisfy the band bounds. -/
+theorem exclude_001000
+    (x0 x1 x2 x3 x4 x5 x6 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h0 : b ≤ x0 ∧ 4*x0 ≤ 21*b)
+    (h6 : b ≤ x6 ∧ 4*x6 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6⟩ := parameters_001000 x0 x1 x2 x3 x4 x5 x6 r0 r1 r2 r3 r4 r5
+  clear r0 r1 r2 r3 r4 r5
+  omega
+
+/-- Terminal branch `00100100` cannot satisfy the band bounds. -/
+theorem exclude_00100100
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h0 : b ≤ x0 ∧ 4*x0 ≤ 21*b)
+    (h8 : b ≤ x8 ∧ 4*x8 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8⟩ := parameters_00100100 x0 x1 x2 x3 x4 x5 x6 x7 x8 r0 r1 r2 r3 r4 r5 r6 r7
+  clear r0 r1 r2 r3 r4 r5 r6 r7
+  omega
+
+/-- Terminal branch `0010010100` cannot satisfy the band bounds. -/
+theorem exclude_0010010100
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h0 : b ≤ x0 ∧ 4*x0 ≤ 21*b)
+    (h5 : b ≤ x5 ∧ 4*x5 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10⟩ := parameters_0010010100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  omega
+
+/-- Terminal branch `0010010101` cannot satisfy the band bounds. -/
+theorem exclude_0010010101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h5 : b ≤ x5 ∧ 4*x5 ≤ 21*b)
+    (h10 : b ≤ x10 ∧ 4*x10 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10⟩ := parameters_0010010101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  omega
+
+/-- Terminal branch `001001011` cannot satisfy the band bounds. -/
+theorem exclude_001001011
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8⟩ := parameters_00100101 x0 x1 x2 x3 x4 x5 x6 x7 x8 r0 r1 r2 r3 r4 r5 r6 r7
+  have hparity := r8.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8
+  omega
+
+/-- Terminal branch `0010011` cannot satisfy the band bounds. -/
+theorem exclude_0010011
+    (x0 x1 x2 x3 x4 x5 x6 x7 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6⟩ := parameters_001001 x0 x1 x2 x3 x4 x5 x6 r0 r1 r2 r3 r4 r5
+  have hparity := r6.2
+  clear r0 r1 r2 r3 r4 r5 r6
+  omega
+
+/-- Terminal branch `00101000` cannot satisfy the band bounds. -/
+theorem exclude_00101000
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h0 : b ≤ x0 ∧ 4*x0 ≤ 21*b)
+    (h8 : b ≤ x8 ∧ 4*x8 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8⟩ := parameters_00101000 x0 x1 x2 x3 x4 x5 x6 x7 x8 r0 r1 r2 r3 r4 r5 r6 r7
+  clear r0 r1 r2 r3 r4 r5 r6 r7
+  omega
+
+/-- Terminal branch `00101001000` cannot satisfy the band bounds. -/
+theorem exclude_00101001000
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h0 : b ≤ x0 ∧ 4*x0 ≤ 21*b)
+    (h11 : b ≤ x11 ∧ 4*x11 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11⟩ := parameters_00101001000 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  omega
+
+/-- Terminal branch `00101001001` cannot satisfy the band bounds. -/
+theorem exclude_00101001001
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h5 : b ≤ x5 ∧ 4*x5 ≤ 21*b)
+    (h10 : b ≤ x10 ∧ 4*x10 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (x11 = 3*x10+1 ∧ x10%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11⟩ := parameters_00101001001 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  omega
+
+/-- Terminal branch `0010100101000` cannot satisfy the band bounds. -/
+theorem exclude_0010100101000
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h0 : b ≤ x0 ∧ 4*x0 ≤ 21*b)
+    (h13 : b ≤ x13 ∧ 4*x13 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13⟩ := parameters_0010100101000 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12
+  omega
+
+/-- Terminal branch `001010010100100` cannot satisfy the band bounds. -/
+theorem exclude_001010010100100
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h10 : b ≤ x10 ∧ 4*x10 ≤ 21*b)
+    (h15 : b ≤ x15 ∧ 4*x15 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    (r12 : (x13 = 3*x12+1 ∧ x12%2 = 1))
+    (r13 : (2*x14 = x13 ∧ x13%2 = 0))
+    (r14 : (2*x15 = x14 ∧ x14%2 = 0))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15⟩ := parameters_001010010100100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14
+  omega
+
+/-- Terminal branch `001010010100101` cannot satisfy the band bounds. -/
+theorem exclude_001010010100101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h2 : b ≤ x2 ∧ 4*x2 ≤ 21*b)
+    (h15 : b ≤ x15 ∧ 4*x15 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    (r12 : (x13 = 3*x12+1 ∧ x12%2 = 1))
+    (r13 : (2*x14 = x13 ∧ x13%2 = 0))
+    (r14 : (x15 = 3*x14+1 ∧ x14%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15⟩ := parameters_001010010100101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14
+  omega
+
+/-- Terminal branch `00101001010011` cannot satisfy the band bounds. -/
+theorem exclude_00101001010011
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    (r12 : (x13 = 3*x12+1 ∧ x12%2 = 1))
+    (r13 : (x14 = 3*x13+1 ∧ x13%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13⟩ := parameters_0010100101001 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12
+  have hparity := r13.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13
+  omega
+
+/-- Terminal branch `001010010101` cannot satisfy the band bounds. -/
+theorem exclude_001010010101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h2 : b ≤ x2 ∧ 4*x2 ≤ 21*b)
+    (h12 : b ≤ x12 ∧ 4*x12 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (x12 = 3*x11+1 ∧ x11%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12⟩ := parameters_001010010101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11
+  omega
+
+/-- Terminal branch `00101001011` cannot satisfy the band bounds. -/
+theorem exclude_00101001011
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (x11 = 3*x10+1 ∧ x10%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10⟩ := parameters_0010100101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  have hparity := r10.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  omega
+
+/-- Terminal branch `001010011` cannot satisfy the band bounds. -/
+theorem exclude_001010011
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8⟩ := parameters_00101001 x0 x1 x2 x3 x4 x5 x6 x7 x8 r0 r1 r2 r3 r4 r5 r6 r7
+  have hparity := r8.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8
+  omega
+
+/-- Terminal branch `0010101` cannot satisfy the band bounds. -/
+theorem exclude_0010101
+    (x0 x1 x2 x3 x4 x5 x6 x7 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h2 : b ≤ x2 ∧ 4*x2 ≤ 21*b)
+    (h7 : b ≤ x7 ∧ 4*x7 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7⟩ := parameters_0010101 x0 x1 x2 x3 x4 x5 x6 x7 r0 r1 r2 r3 r4 r5 r6
+  clear r0 r1 r2 r3 r4 r5 r6
+  omega
+
+/-- Terminal branch `001011` cannot satisfy the band bounds. -/
+theorem exclude_001011
+    (x0 x1 x2 x3 x4 x5 x6 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5⟩ := parameters_00101 x0 x1 x2 x3 x4 x5 r0 r1 r2 r3 r4
+  have hparity := r5.2
+  clear r0 r1 r2 r3 r4 r5
+  omega
+
+/-- Terminal branch `0011` cannot satisfy the band bounds. -/
+theorem exclude_0011
+    (x0 x1 x2 x3 x4 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3⟩ := parameters_001 x0 x1 x2 x3 r0 r1 r2
+  have hparity := r3.2
+  clear r0 r1 r2 r3
+  omega
+
+/-- Terminal branch `01000` cannot satisfy the band bounds. -/
+theorem exclude_01000
+    (x0 x1 x2 x3 x4 x5 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h2 : b ≤ x2 ∧ 4*x2 ≤ 21*b)
+    (h5 : b ≤ x5 ∧ 4*x5 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5⟩ := parameters_01000 x0 x1 x2 x3 x4 x5 r0 r1 r2 r3 r4
+  clear r0 r1 r2 r3 r4
+  omega
+
+/-- Terminal branch `01001000` cannot satisfy the band bounds. -/
+theorem exclude_01001000
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h0 : b ≤ x0 ∧ 4*x0 ≤ 21*b)
+    (h8 : b ≤ x8 ∧ 4*x8 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8⟩ := parameters_01001000 x0 x1 x2 x3 x4 x5 x6 x7 x8 r0 r1 r2 r3 r4 r5 r6 r7
+  clear r0 r1 r2 r3 r4 r5 r6 r7
+  omega
+
+/-- Terminal branch `01001001` cannot satisfy the band bounds. -/
+theorem exclude_01001001
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h2 : b ≤ x2 ∧ 4*x2 ≤ 21*b)
+    (h7 : b ≤ x7 ∧ 4*x7 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8⟩ := parameters_01001001 x0 x1 x2 x3 x4 x5 x6 x7 x8 r0 r1 r2 r3 r4 r5 r6 r7
+  clear r0 r1 r2 r3 r4 r5 r6 r7
+  omega
+
+/-- Terminal branch `0100101000` cannot satisfy the band bounds. -/
+theorem exclude_0100101000
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h2 : b ≤ x2 ∧ 4*x2 ≤ 21*b)
+    (h10 : b ≤ x10 ∧ 4*x10 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10⟩ := parameters_0100101000 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  omega
+
+/-- Terminal branch `010010100100` cannot satisfy the band bounds. -/
+theorem exclude_010010100100
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h7 : b ≤ x7 ∧ 4*x7 ≤ 21*b)
+    (h12 : b ≤ x12 ∧ 4*x12 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12⟩ := parameters_010010100100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11
+  omega
+
+/-- Terminal branch `010010100101000` cannot satisfy the band bounds. -/
+theorem exclude_010010100101000
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h2 : b ≤ x2 ∧ 4*x2 ≤ 21*b)
+    (h15 : b ≤ x15 ∧ 4*x15 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (x12 = 3*x11+1 ∧ x11%2 = 1))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    (r13 : (2*x14 = x13 ∧ x13%2 = 0))
+    (r14 : (2*x15 = x14 ∧ x14%2 = 0))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15⟩ := parameters_010010100101000 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14
+  omega
+
+/-- Terminal branch `01001010010100100` cannot satisfy the band bounds. -/
+theorem exclude_01001010010100100
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h12 : b ≤ x12 ∧ 4*x12 ≤ 21*b)
+    (h17 : b ≤ x17 ∧ 4*x17 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (x12 = 3*x11+1 ∧ x11%2 = 1))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    (r13 : (2*x14 = x13 ∧ x13%2 = 0))
+    (r14 : (x15 = 3*x14+1 ∧ x14%2 = 1))
+    (r15 : (2*x16 = x15 ∧ x15%2 = 0))
+    (r16 : (2*x17 = x16 ∧ x16%2 = 0))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17⟩ := parameters_01001010010100100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14 r15 r16
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14 r15 r16
+  omega
+
+/-- Terminal branch `01001010010100101` cannot satisfy the band bounds. -/
+theorem exclude_01001010010100101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h4 : b ≤ x4 ∧ 4*x4 ≤ 21*b)
+    (h17 : b ≤ x17 ∧ 4*x17 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (x12 = 3*x11+1 ∧ x11%2 = 1))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    (r13 : (2*x14 = x13 ∧ x13%2 = 0))
+    (r14 : (x15 = 3*x14+1 ∧ x14%2 = 1))
+    (r15 : (2*x16 = x15 ∧ x15%2 = 0))
+    (r16 : (x17 = 3*x16+1 ∧ x16%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17⟩ := parameters_01001010010100101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14 r15 r16
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14 r15 r16
+  omega
+
+/-- Terminal branch `0100101001010011` cannot satisfy the band bounds. -/
+theorem exclude_0100101001010011
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (x12 = 3*x11+1 ∧ x11%2 = 1))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    (r13 : (2*x14 = x13 ∧ x13%2 = 0))
+    (r14 : (x15 = 3*x14+1 ∧ x14%2 = 1))
+    (r15 : (x16 = 3*x15+1 ∧ x15%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15⟩ := parameters_010010100101001 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14
+  have hparity := r15.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14 r15
+  omega
+
+/-- Terminal branch `01001010010101` cannot satisfy the band bounds. -/
+theorem exclude_01001010010101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h1 : b ≤ x1 ∧ 4*x1 ≤ 21*b)
+    (h14 : b ≤ x14 ∧ 4*x14 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (x12 = 3*x11+1 ∧ x11%2 = 1))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    (r13 : (x14 = 3*x13+1 ∧ x13%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14⟩ := parameters_01001010010101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13
+  omega
+
+/-- Terminal branch `0100101001011` cannot satisfy the band bounds. -/
+theorem exclude_0100101001011
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (x12 = 3*x11+1 ∧ x11%2 = 1))
+    (r12 : (x13 = 3*x12+1 ∧ x12%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12⟩ := parameters_010010100101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11
+  have hparity := r12.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12
+  omega
+
+/-- Terminal branch `01001010011` cannot satisfy the band bounds. -/
+theorem exclude_01001010011
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (x11 = 3*x10+1 ∧ x10%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10⟩ := parameters_0100101001 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  have hparity := r10.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  omega
+
+/-- Terminal branch `010010101` cannot satisfy the band bounds. -/
+theorem exclude_010010101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h4 : b ≤ x4 ∧ 4*x4 ≤ 21*b)
+    (h9 : b ≤ x9 ∧ 4*x9 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9⟩ := parameters_010010101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 r0 r1 r2 r3 r4 r5 r6 r7 r8
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8
+  omega
+
+/-- Terminal branch `01001011` cannot satisfy the band bounds. -/
+theorem exclude_01001011
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7⟩ := parameters_0100101 x0 x1 x2 x3 x4 x5 x6 x7 r0 r1 r2 r3 r4 r5 r6
+  have hparity := r7.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7
+  omega
+
+/-- Terminal branch `010011` cannot satisfy the band bounds. -/
+theorem exclude_010011
+    (x0 x1 x2 x3 x4 x5 x6 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5⟩ := parameters_01001 x0 x1 x2 x3 x4 x5 r0 r1 r2 r3 r4
+  have hparity := r5.2
+  clear r0 r1 r2 r3 r4 r5
+  omega
+
+/-- Terminal branch `0101000` cannot satisfy the band bounds. -/
+theorem exclude_0101000
+    (x0 x1 x2 x3 x4 x5 x6 x7 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h4 : b ≤ x4 ∧ 4*x4 ≤ 21*b)
+    (h7 : b ≤ x7 ∧ 4*x7 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7⟩ := parameters_0101000 x0 x1 x2 x3 x4 x5 x6 x7 r0 r1 r2 r3 r4 r5 r6
+  clear r0 r1 r2 r3 r4 r5 r6
+  omega
+
+/-- Terminal branch `0101001000` cannot satisfy the band bounds. -/
+theorem exclude_0101001000
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h2 : b ≤ x2 ∧ 4*x2 ≤ 21*b)
+    (h10 : b ≤ x10 ∧ 4*x10 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10⟩ := parameters_0101001000 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  omega
+
+/-- Terminal branch `0101001001` cannot satisfy the band bounds. -/
+theorem exclude_0101001001
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h4 : b ≤ x4 ∧ 4*x4 ≤ 21*b)
+    (h9 : b ≤ x9 ∧ 4*x9 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10⟩ := parameters_0101001001 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  omega
+
+/-- Terminal branch `010100101000` cannot satisfy the band bounds. -/
+theorem exclude_010100101000
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h4 : b ≤ x4 ∧ 4*x4 ≤ 21*b)
+    (h12 : b ≤ x12 ∧ 4*x12 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12⟩ := parameters_010100101000 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11
+  omega
+
+/-- Terminal branch `01010010100100` cannot satisfy the band bounds. -/
+theorem exclude_01010010100100
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h9 : b ≤ x9 ∧ 4*x9 ≤ 21*b)
+    (h14 : b ≤ x14 ∧ 4*x14 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (x12 = 3*x11+1 ∧ x11%2 = 1))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    (r13 : (2*x14 = x13 ∧ x13%2 = 0))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14⟩ := parameters_01010010100100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13
+  omega
+
+/-- Terminal branch `01010010100101` cannot satisfy the band bounds. -/
+theorem exclude_01010010100101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h1 : b ≤ x1 ∧ 4*x1 ≤ 21*b)
+    (h14 : b ≤ x14 ∧ 4*x14 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (x12 = 3*x11+1 ∧ x11%2 = 1))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    (r13 : (x14 = 3*x13+1 ∧ x13%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14⟩ := parameters_01010010100101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13
+  omega
+
+/-- Terminal branch `0101001010011` cannot satisfy the band bounds. -/
+theorem exclude_0101001010011
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    (r11 : (x12 = 3*x11+1 ∧ x11%2 = 1))
+    (r12 : (x13 = 3*x12+1 ∧ x12%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12⟩ := parameters_010100101001 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11
+  have hparity := r12.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12
+  omega
+
+/-- Terminal branch `01010010101` cannot satisfy the band bounds. -/
+theorem exclude_01010010101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h1 : b ≤ x1 ∧ 4*x1 ≤ 21*b)
+    (h11 : b ≤ x11 ∧ 4*x11 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (x11 = 3*x10+1 ∧ x10%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11⟩ := parameters_01010010101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  omega
+
+/-- Terminal branch `0101001011` cannot satisfy the band bounds. -/
+theorem exclude_0101001011
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9⟩ := parameters_010100101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 r0 r1 r2 r3 r4 r5 r6 r7 r8
+  have hparity := r9.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  omega
+
+/-- Terminal branch `01010011` cannot satisfy the band bounds. -/
+theorem exclude_01010011
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7⟩ := parameters_0101001 x0 x1 x2 x3 x4 x5 x6 x7 r0 r1 r2 r3 r4 r5 r6
+  have hparity := r7.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7
+  omega
+
+/-- Terminal branch `010101` cannot satisfy the band bounds. -/
+theorem exclude_010101
+    (x0 x1 x2 x3 x4 x5 x6 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h1 : b ≤ x1 ∧ 4*x1 ≤ 21*b)
+    (h6 : b ≤ x6 ∧ 4*x6 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6⟩ := parameters_010101 x0 x1 x2 x3 x4 x5 x6 r0 r1 r2 r3 r4 r5
+  clear r0 r1 r2 r3 r4 r5
+  omega
+
+/-- Terminal branch `01011` cannot satisfy the band bounds. -/
+theorem exclude_01011
+    (x0 x1 x2 x3 x4 x5 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4⟩ := parameters_0101 x0 x1 x2 x3 x4 r0 r1 r2 r3
+  have hparity := r4.2
+  clear r0 r1 r2 r3 r4
+  omega
+
+/-- Terminal branch `011` cannot satisfy the band bounds. -/
+theorem exclude_011
+    (x0 x1 x2 x3 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2⟩ := parameters_01 x0 x1 x2 r0 r1
+  have hparity := r2.2
+  clear r0 r1 r2
+  omega
+
+/-- Terminal branch `1000` cannot satisfy the band bounds. -/
+theorem exclude_1000
+    (x0 x1 x2 x3 x4 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h1 : b ≤ x1 ∧ 4*x1 ≤ 21*b)
+    (h4 : b ≤ x4 ∧ 4*x4 ≤ 21*b)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4⟩ := parameters_1000 x0 x1 x2 x3 x4 r0 r1 r2 r3
+  clear r0 r1 r2 r3
+  omega
+
+/-- Terminal branch `1001000` cannot satisfy the band bounds. -/
+theorem exclude_1001000
+    (x0 x1 x2 x3 x4 x5 x6 x7 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h1 : b ≤ x1 ∧ 4*x1 ≤ 21*b)
+    (h7 : b ≤ x7 ∧ 4*x7 ≤ 21*b)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7⟩ := parameters_1001000 x0 x1 x2 x3 x4 x5 x6 x7 r0 r1 r2 r3 r4 r5 r6
+  clear r0 r1 r2 r3 r4 r5 r6
+  omega
+
+/-- Terminal branch `1001001` cannot satisfy the band bounds. -/
+theorem exclude_1001001
+    (x0 x1 x2 x3 x4 x5 x6 x7 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h1 : b ≤ x1 ∧ 4*x1 ≤ 21*b)
+    (h6 : b ≤ x6 ∧ 4*x6 ≤ 21*b)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7⟩ := parameters_1001001 x0 x1 x2 x3 x4 x5 x6 x7 r0 r1 r2 r3 r4 r5 r6
+  clear r0 r1 r2 r3 r4 r5 r6
+  omega
+
+/-- Terminal branch `100101000` cannot satisfy the band bounds. -/
+theorem exclude_100101000
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h1 : b ≤ x1 ∧ 4*x1 ≤ 21*b)
+    (h9 : b ≤ x9 ∧ 4*x9 ≤ 21*b)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9⟩ := parameters_100101000 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 r0 r1 r2 r3 r4 r5 r6 r7 r8
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8
+  omega
+
+/-- Terminal branch `10010100100` cannot satisfy the band bounds. -/
+theorem exclude_10010100100
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h6 : b ≤ x6 ∧ 4*x6 ≤ 21*b)
+    (h11 : b ≤ x11 ∧ 4*x11 ≤ 21*b)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11⟩ := parameters_10010100100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  omega
+
+/-- Terminal branch `10010100101000` cannot satisfy the band bounds. -/
+theorem exclude_10010100101000
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h1 : b ≤ x1 ∧ 4*x1 ≤ 21*b)
+    (h14 : b ≤ x14 ∧ 4*x14 ≤ 21*b)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (x11 = 3*x10+1 ∧ x10%2 = 1))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    (r13 : (2*x14 = x13 ∧ x13%2 = 0))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14⟩ := parameters_10010100101000 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13
+  omega
+
+/-- Terminal branch `1001010010100100` cannot satisfy the band bounds. -/
+theorem exclude_1001010010100100
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h11 : b ≤ x11 ∧ 4*x11 ≤ 21*b)
+    (h16 : b ≤ x16 ∧ 4*x16 ≤ 21*b)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (x11 = 3*x10+1 ∧ x10%2 = 1))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    (r13 : (x14 = 3*x13+1 ∧ x13%2 = 1))
+    (r14 : (2*x15 = x14 ∧ x14%2 = 0))
+    (r15 : (2*x16 = x15 ∧ x15%2 = 0))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16⟩ := parameters_1001010010100100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14 r15
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14 r15
+  omega
+
+/-- Terminal branch `1001010010100101` cannot satisfy the band bounds. -/
+theorem exclude_1001010010100101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h3 : b ≤ x3 ∧ 4*x3 ≤ 21*b)
+    (h16 : b ≤ x16 ∧ 4*x16 ≤ 21*b)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (x11 = 3*x10+1 ∧ x10%2 = 1))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    (r13 : (x14 = 3*x13+1 ∧ x13%2 = 1))
+    (r14 : (2*x15 = x14 ∧ x14%2 = 0))
+    (r15 : (x16 = 3*x15+1 ∧ x15%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16⟩ := parameters_1001010010100101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14 r15
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14 r15
+  omega
+
+/-- Terminal branch `100101001010011` cannot satisfy the band bounds. -/
+theorem exclude_100101001010011
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (x11 = 3*x10+1 ∧ x10%2 = 1))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    (r13 : (x14 = 3*x13+1 ∧ x13%2 = 1))
+    (r14 : (x15 = 3*x14+1 ∧ x14%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14⟩ := parameters_10010100101001 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13
+  have hparity := r14.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14
+  omega
+
+/-- Terminal branch `1001010010101` cannot satisfy the band bounds. -/
+theorem exclude_1001010010101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h0 : b ≤ x0 ∧ 4*x0 ≤ 21*b)
+    (h13 : b ≤ x13 ∧ 4*x13 ≤ 21*b)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (x11 = 3*x10+1 ∧ x10%2 = 1))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    (r12 : (x13 = 3*x12+1 ∧ x12%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13⟩ := parameters_1001010010101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12
+  omega
+
+/-- Terminal branch `100101001011` cannot satisfy the band bounds. -/
+theorem exclude_100101001011
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (x11 = 3*x10+1 ∧ x10%2 = 1))
+    (r11 : (x12 = 3*x11+1 ∧ x11%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11⟩ := parameters_10010100101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  have hparity := r11.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11
+  omega
+
+/-- Terminal branch `1001010011` cannot satisfy the band bounds. -/
+theorem exclude_1001010011
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9⟩ := parameters_100101001 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 r0 r1 r2 r3 r4 r5 r6 r7 r8
+  have hparity := r9.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  omega
+
+/-- Terminal branch `10010101` cannot satisfy the band bounds. -/
+theorem exclude_10010101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h3 : b ≤ x3 ∧ 4*x3 ≤ 21*b)
+    (h8 : b ≤ x8 ∧ 4*x8 ≤ 21*b)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8⟩ := parameters_10010101 x0 x1 x2 x3 x4 x5 x6 x7 x8 r0 r1 r2 r3 r4 r5 r6 r7
+  clear r0 r1 r2 r3 r4 r5 r6 r7
+  omega
+
+/-- Terminal branch `1001011` cannot satisfy the band bounds. -/
+theorem exclude_1001011
+    (x0 x1 x2 x3 x4 x5 x6 x7 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6⟩ := parameters_100101 x0 x1 x2 x3 x4 x5 x6 r0 r1 r2 r3 r4 r5
+  have hparity := r6.2
+  clear r0 r1 r2 r3 r4 r5 r6
+  omega
+
+/-- Terminal branch `10011` cannot satisfy the band bounds. -/
+theorem exclude_10011
+    (x0 x1 x2 x3 x4 x5 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4⟩ := parameters_1001 x0 x1 x2 x3 x4 r0 r1 r2 r3
+  have hparity := r4.2
+  clear r0 r1 r2 r3 r4
+  omega
+
+/-- Terminal branch `101000` cannot satisfy the band bounds. -/
+theorem exclude_101000
+    (x0 x1 x2 x3 x4 x5 x6 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h3 : b ≤ x3 ∧ 4*x3 ≤ 21*b)
+    (h6 : b ≤ x6 ∧ 4*x6 ≤ 21*b)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6⟩ := parameters_101000 x0 x1 x2 x3 x4 x5 x6 r0 r1 r2 r3 r4 r5
+  clear r0 r1 r2 r3 r4 r5
+  omega
+
+/-- Terminal branch `101001000` cannot satisfy the band bounds. -/
+theorem exclude_101001000
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h1 : b ≤ x1 ∧ 4*x1 ≤ 21*b)
+    (h9 : b ≤ x9 ∧ 4*x9 ≤ 21*b)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9⟩ := parameters_101001000 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 r0 r1 r2 r3 r4 r5 r6 r7 r8
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8
+  omega
+
+/-- Terminal branch `101001001` cannot satisfy the band bounds. -/
+theorem exclude_101001001
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h3 : b ≤ x3 ∧ 4*x3 ≤ 21*b)
+    (h8 : b ≤ x8 ∧ 4*x8 ≤ 21*b)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9⟩ := parameters_101001001 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 r0 r1 r2 r3 r4 r5 r6 r7 r8
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8
+  omega
+
+/-- Terminal branch `10100101000` cannot satisfy the band bounds. -/
+theorem exclude_10100101000
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h3 : b ≤ x3 ∧ 4*x3 ≤ 21*b)
+    (h11 : b ≤ x11 ∧ 4*x11 ≤ 21*b)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11⟩ := parameters_10100101000 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  omega
+
+/-- Terminal branch `1010010100100` cannot satisfy the band bounds. -/
+theorem exclude_1010010100100
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h8 : b ≤ x8 ∧ 4*x8 ≤ 21*b)
+    (h13 : b ≤ x13 ∧ 4*x13 ≤ 21*b)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (x11 = 3*x10+1 ∧ x10%2 = 1))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13⟩ := parameters_1010010100100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12
+  omega
+
+/-- Terminal branch `1010010100101` cannot satisfy the band bounds. -/
+theorem exclude_1010010100101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h0 : b ≤ x0 ∧ 4*x0 ≤ 21*b)
+    (h13 : b ≤ x13 ∧ 4*x13 ≤ 21*b)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (x11 = 3*x10+1 ∧ x10%2 = 1))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0))
+    (r12 : (x13 = 3*x12+1 ∧ x12%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13⟩ := parameters_1010010100101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12
+  omega
+
+/-- Terminal branch `101001010011` cannot satisfy the band bounds. -/
+theorem exclude_101001010011
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0))
+    (r10 : (x11 = 3*x10+1 ∧ x10%2 = 1))
+    (r11 : (x12 = 3*x11+1 ∧ x11%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11⟩ := parameters_10100101001 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
+  have hparity := r11.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11
+  omega
+
+/-- Terminal branch `1010010101` cannot satisfy the band bounds. -/
+theorem exclude_1010010101
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h0 : b ≤ x0 ∧ 4*x0 ≤ 21*b)
+    (h10 : b ≤ x10 ∧ 4*x10 ≤ 21*b)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0))
+    (r9 : (x10 = 3*x9+1 ∧ x9%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10⟩ := parameters_1010010101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8 r9
+  omega
+
+/-- Terminal branch `101001011` cannot satisfy the band bounds. -/
+theorem exclude_101001011
+    (x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0))
+    (r7 : (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (x9 = 3*x8+1 ∧ x8%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6,p7,p8⟩ := parameters_10100101 x0 x1 x2 x3 x4 x5 x6 x7 x8 r0 r1 r2 r3 r4 r5 r6 r7
+  have hparity := r8.2
+  clear r0 r1 r2 r3 r4 r5 r6 r7 r8
+  omega
+
+/-- Terminal branch `1010011` cannot satisfy the band bounds. -/
+theorem exclude_1010011
+    (x0 x1 x2 x3 x4 x5 x6 x7 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0))
+    (r5 : (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (x7 = 3*x6+1 ∧ x6%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5,p6⟩ := parameters_101001 x0 x1 x2 x3 x4 x5 x6 r0 r1 r2 r3 r4 r5
+  have hparity := r6.2
+  clear r0 r1 r2 r3 r4 r5 r6
+  omega
+
+/-- Terminal branch `10101` cannot satisfy the band bounds. -/
+theorem exclude_10101
+    (x0 x1 x2 x3 x4 x5 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (h0 : b ≤ x0 ∧ 4*x0 ≤ 21*b)
+    (h5 : b ≤ x5 ∧ 4*x5 ≤ 21*b)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0))
+    (r4 : (x5 = 3*x4+1 ∧ x4%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3,p4,p5⟩ := parameters_10101 x0 x1 x2 x3 x4 x5 r0 r1 r2 r3 r4
+  clear r0 r1 r2 r3 r4
+  omega
+
+/-- Terminal branch `1011` cannot satisfy the band bounds. -/
+theorem exclude_1011
+    (x0 x1 x2 x3 x4 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0))
+    (r2 : (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (x4 = 3*x3+1 ∧ x3%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1,p2,p3⟩ := parameters_101 x0 x1 x2 x3 r0 r1 r2
+  have hparity := r3.2
+  clear r0 r1 r2 r3
+  omega
+
+/-- Terminal branch `11` cannot satisfy the band bounds. -/
+theorem exclude_11
+    (x0 x1 x2 : Nat)
+    (b : Nat) (hb : 1 < b)
+    (r0 : (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (x2 = 3*x1+1 ∧ x1%2 = 1))
+    : False := by
+  obtain ⟨q,p0,p1⟩ := parameters_1 x0 x1 r0
+  have hparity := r1.2
+  clear r0 r1
+  omega
+
+theorem impossible_trace
+    (b x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 : Nat) (hb : 1 < b)
+    (h0 : b ≤ x0 ∧ 4*x0 ≤ 21*b)
+    (h1 : b ≤ x1 ∧ 4*x1 ≤ 21*b)
+    (h2 : b ≤ x2 ∧ 4*x2 ≤ 21*b)
+    (h3 : b ≤ x3 ∧ 4*x3 ≤ 21*b)
+    (h4 : b ≤ x4 ∧ 4*x4 ≤ 21*b)
+    (h5 : b ≤ x5 ∧ 4*x5 ≤ 21*b)
+    (h6 : b ≤ x6 ∧ 4*x6 ≤ 21*b)
+    (h7 : b ≤ x7 ∧ 4*x7 ≤ 21*b)
+    (h8 : b ≤ x8 ∧ 4*x8 ≤ 21*b)
+    (h9 : b ≤ x9 ∧ 4*x9 ≤ 21*b)
+    (h10 : b ≤ x10 ∧ 4*x10 ≤ 21*b)
+    (h11 : b ≤ x11 ∧ 4*x11 ≤ 21*b)
+    (h12 : b ≤ x12 ∧ 4*x12 ≤ 21*b)
+    (h13 : b ≤ x13 ∧ 4*x13 ≤ 21*b)
+    (h14 : b ≤ x14 ∧ 4*x14 ≤ 21*b)
+    (h15 : b ≤ x15 ∧ 4*x15 ≤ 21*b)
+    (h16 : b ≤ x16 ∧ 4*x16 ≤ 21*b)
+    (h17 : b ≤ x17 ∧ 4*x17 ≤ 21*b)
+    (r0 : (2*x1 = x0 ∧ x0%2 = 0) ∨ (x1 = 3*x0+1 ∧ x0%2 = 1))
+    (r1 : (2*x2 = x1 ∧ x1%2 = 0) ∨ (x2 = 3*x1+1 ∧ x1%2 = 1))
+    (r2 : (2*x3 = x2 ∧ x2%2 = 0) ∨ (x3 = 3*x2+1 ∧ x2%2 = 1))
+    (r3 : (2*x4 = x3 ∧ x3%2 = 0) ∨ (x4 = 3*x3+1 ∧ x3%2 = 1))
+    (r4 : (2*x5 = x4 ∧ x4%2 = 0) ∨ (x5 = 3*x4+1 ∧ x4%2 = 1))
+    (r5 : (2*x6 = x5 ∧ x5%2 = 0) ∨ (x6 = 3*x5+1 ∧ x5%2 = 1))
+    (r6 : (2*x7 = x6 ∧ x6%2 = 0) ∨ (x7 = 3*x6+1 ∧ x6%2 = 1))
+    (r7 : (2*x8 = x7 ∧ x7%2 = 0) ∨ (x8 = 3*x7+1 ∧ x7%2 = 1))
+    (r8 : (2*x9 = x8 ∧ x8%2 = 0) ∨ (x9 = 3*x8+1 ∧ x8%2 = 1))
+    (r9 : (2*x10 = x9 ∧ x9%2 = 0) ∨ (x10 = 3*x9+1 ∧ x9%2 = 1))
+    (r10 : (2*x11 = x10 ∧ x10%2 = 0) ∨ (x11 = 3*x10+1 ∧ x10%2 = 1))
+    (r11 : (2*x12 = x11 ∧ x11%2 = 0) ∨ (x12 = 3*x11+1 ∧ x11%2 = 1))
+    (r12 : (2*x13 = x12 ∧ x12%2 = 0) ∨ (x13 = 3*x12+1 ∧ x12%2 = 1))
+    (r13 : (2*x14 = x13 ∧ x13%2 = 0) ∨ (x14 = 3*x13+1 ∧ x13%2 = 1))
+    (r14 : (2*x15 = x14 ∧ x14%2 = 0) ∨ (x15 = 3*x14+1 ∧ x14%2 = 1))
+    (r15 : (2*x16 = x15 ∧ x15%2 = 0) ∨ (x16 = 3*x15+1 ∧ x15%2 = 1))
+    (r16 : (2*x17 = x16 ∧ x16%2 = 0) ∨ (x17 = 3*x16+1 ∧ x16%2 = 1))
+    : False := by
+  revert r16 r15 r14 r13 r12 r11 r10 r9 r8 r7 r6 r5 r4 r3 r2 r1 r0
+  intro r0
+  rcases r0 with r0 | r0
+  · -- branch 0 at time 0
+    intro r1
+    rcases r1 with r1 | r1
+    · -- branch 0 at time 1
+      intro r2
+      rcases r2 with r2 | r2
+      · -- branch 0 at time 2
+        exact False.elim (exclude_000 x0 x1 x2 x3 b hb h0 h3 r0 r1 r2)
+      · -- branch 1 at time 2
+        intro r3
+        rcases r3 with r3 | r3
+        · -- branch 0 at time 3
+          intro r4
+          rcases r4 with r4 | r4
+          · -- branch 0 at time 4
+            intro r5
+            rcases r5 with r5 | r5
+            · -- branch 0 at time 5
+              exact False.elim (exclude_001000 x0 x1 x2 x3 x4 x5 x6 b hb h0 h6 r0 r1 r2 r3 r4 r5)
+            · -- branch 1 at time 5
+              intro r6
+              rcases r6 with r6 | r6
+              · -- branch 0 at time 6
+                intro r7
+                rcases r7 with r7 | r7
+                · -- branch 0 at time 7
+                  exact False.elim (exclude_00100100 x0 x1 x2 x3 x4 x5 x6 x7 x8 b hb h0 h8 r0 r1 r2 r3 r4 r5 r6 r7)
+                · -- branch 1 at time 7
+                  intro r8
+                  rcases r8 with r8 | r8
+                  · -- branch 0 at time 8
+                    intro r9
+                    rcases r9 with r9 | r9
+                    · -- branch 0 at time 9
+                      exact False.elim (exclude_0010010100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 b hb h0 h5 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9)
+                    · -- branch 1 at time 9
+                      exact False.elim (exclude_0010010101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 b hb h5 h10 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9)
+                  · -- branch 1 at time 8
+                    exact False.elim (exclude_001001011 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 b hb r0 r1 r2 r3 r4 r5 r6 r7 r8)
+              · -- branch 1 at time 6
+                exact False.elim (exclude_0010011 x0 x1 x2 x3 x4 x5 x6 x7 b hb r0 r1 r2 r3 r4 r5 r6)
+          · -- branch 1 at time 4
+            intro r5
+            rcases r5 with r5 | r5
+            · -- branch 0 at time 5
+              intro r6
+              rcases r6 with r6 | r6
+              · -- branch 0 at time 6
+                intro r7
+                rcases r7 with r7 | r7
+                · -- branch 0 at time 7
+                  exact False.elim (exclude_00101000 x0 x1 x2 x3 x4 x5 x6 x7 x8 b hb h0 h8 r0 r1 r2 r3 r4 r5 r6 r7)
+                · -- branch 1 at time 7
+                  intro r8
+                  rcases r8 with r8 | r8
+                  · -- branch 0 at time 8
+                    intro r9
+                    rcases r9 with r9 | r9
+                    · -- branch 0 at time 9
+                      intro r10
+                      rcases r10 with r10 | r10
+                      · -- branch 0 at time 10
+                        exact False.elim (exclude_00101001000 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 b hb h0 h11 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10)
+                      · -- branch 1 at time 10
+                        exact False.elim (exclude_00101001001 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 b hb h5 h10 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10)
+                    · -- branch 1 at time 9
+                      intro r10
+                      rcases r10 with r10 | r10
+                      · -- branch 0 at time 10
+                        intro r11
+                        rcases r11 with r11 | r11
+                        · -- branch 0 at time 11
+                          intro r12
+                          rcases r12 with r12 | r12
+                          · -- branch 0 at time 12
+                            exact False.elim (exclude_0010100101000 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 b hb h0 h13 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12)
+                          · -- branch 1 at time 12
+                            intro r13
+                            rcases r13 with r13 | r13
+                            · -- branch 0 at time 13
+                              intro r14
+                              rcases r14 with r14 | r14
+                              · -- branch 0 at time 14
+                                exact False.elim (exclude_001010010100100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 b hb h10 h15 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14)
+                              · -- branch 1 at time 14
+                                exact False.elim (exclude_001010010100101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 b hb h2 h15 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14)
+                            · -- branch 1 at time 13
+                              exact False.elim (exclude_00101001010011 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 b hb r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13)
+                        · -- branch 1 at time 11
+                          exact False.elim (exclude_001010010101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 b hb h2 h12 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11)
+                      · -- branch 1 at time 10
+                        exact False.elim (exclude_00101001011 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 b hb r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10)
+                  · -- branch 1 at time 8
+                    exact False.elim (exclude_001010011 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 b hb r0 r1 r2 r3 r4 r5 r6 r7 r8)
+              · -- branch 1 at time 6
+                exact False.elim (exclude_0010101 x0 x1 x2 x3 x4 x5 x6 x7 b hb h2 h7 r0 r1 r2 r3 r4 r5 r6)
+            · -- branch 1 at time 5
+              exact False.elim (exclude_001011 x0 x1 x2 x3 x4 x5 x6 b hb r0 r1 r2 r3 r4 r5)
+        · -- branch 1 at time 3
+          exact False.elim (exclude_0011 x0 x1 x2 x3 x4 b hb r0 r1 r2 r3)
+    · -- branch 1 at time 1
+      intro r2
+      rcases r2 with r2 | r2
+      · -- branch 0 at time 2
+        intro r3
+        rcases r3 with r3 | r3
+        · -- branch 0 at time 3
+          intro r4
+          rcases r4 with r4 | r4
+          · -- branch 0 at time 4
+            exact False.elim (exclude_01000 x0 x1 x2 x3 x4 x5 b hb h2 h5 r0 r1 r2 r3 r4)
+          · -- branch 1 at time 4
+            intro r5
+            rcases r5 with r5 | r5
+            · -- branch 0 at time 5
+              intro r6
+              rcases r6 with r6 | r6
+              · -- branch 0 at time 6
+                intro r7
+                rcases r7 with r7 | r7
+                · -- branch 0 at time 7
+                  exact False.elim (exclude_01001000 x0 x1 x2 x3 x4 x5 x6 x7 x8 b hb h0 h8 r0 r1 r2 r3 r4 r5 r6 r7)
+                · -- branch 1 at time 7
+                  exact False.elim (exclude_01001001 x0 x1 x2 x3 x4 x5 x6 x7 x8 b hb h2 h7 r0 r1 r2 r3 r4 r5 r6 r7)
+              · -- branch 1 at time 6
+                intro r7
+                rcases r7 with r7 | r7
+                · -- branch 0 at time 7
+                  intro r8
+                  rcases r8 with r8 | r8
+                  · -- branch 0 at time 8
+                    intro r9
+                    rcases r9 with r9 | r9
+                    · -- branch 0 at time 9
+                      exact False.elim (exclude_0100101000 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 b hb h2 h10 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9)
+                    · -- branch 1 at time 9
+                      intro r10
+                      rcases r10 with r10 | r10
+                      · -- branch 0 at time 10
+                        intro r11
+                        rcases r11 with r11 | r11
+                        · -- branch 0 at time 11
+                          exact False.elim (exclude_010010100100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 b hb h7 h12 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11)
+                        · -- branch 1 at time 11
+                          intro r12
+                          rcases r12 with r12 | r12
+                          · -- branch 0 at time 12
+                            intro r13
+                            rcases r13 with r13 | r13
+                            · -- branch 0 at time 13
+                              intro r14
+                              rcases r14 with r14 | r14
+                              · -- branch 0 at time 14
+                                exact False.elim (exclude_010010100101000 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 b hb h2 h15 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14)
+                              · -- branch 1 at time 14
+                                intro r15
+                                rcases r15 with r15 | r15
+                                · -- branch 0 at time 15
+                                  intro r16
+                                  rcases r16 with r16 | r16
+                                  · -- branch 0 at time 16
+                                    exact False.elim (exclude_01001010010100100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 b hb h12 h17 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14 r15 r16)
+                                  · -- branch 1 at time 16
+                                    exact False.elim (exclude_01001010010100101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 b hb h4 h17 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14 r15 r16)
+                                · -- branch 1 at time 15
+                                  exact False.elim (exclude_0100101001010011 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 b hb r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14 r15)
+                            · -- branch 1 at time 13
+                              exact False.elim (exclude_01001010010101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 b hb h1 h14 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13)
+                          · -- branch 1 at time 12
+                            exact False.elim (exclude_0100101001011 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 b hb r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12)
+                      · -- branch 1 at time 10
+                        exact False.elim (exclude_01001010011 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 b hb r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10)
+                  · -- branch 1 at time 8
+                    exact False.elim (exclude_010010101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 b hb h4 h9 r0 r1 r2 r3 r4 r5 r6 r7 r8)
+                · -- branch 1 at time 7
+                  exact False.elim (exclude_01001011 x0 x1 x2 x3 x4 x5 x6 x7 x8 b hb r0 r1 r2 r3 r4 r5 r6 r7)
+            · -- branch 1 at time 5
+              exact False.elim (exclude_010011 x0 x1 x2 x3 x4 x5 x6 b hb r0 r1 r2 r3 r4 r5)
+        · -- branch 1 at time 3
+          intro r4
+          rcases r4 with r4 | r4
+          · -- branch 0 at time 4
+            intro r5
+            rcases r5 with r5 | r5
+            · -- branch 0 at time 5
+              intro r6
+              rcases r6 with r6 | r6
+              · -- branch 0 at time 6
+                exact False.elim (exclude_0101000 x0 x1 x2 x3 x4 x5 x6 x7 b hb h4 h7 r0 r1 r2 r3 r4 r5 r6)
+              · -- branch 1 at time 6
+                intro r7
+                rcases r7 with r7 | r7
+                · -- branch 0 at time 7
+                  intro r8
+                  rcases r8 with r8 | r8
+                  · -- branch 0 at time 8
+                    intro r9
+                    rcases r9 with r9 | r9
+                    · -- branch 0 at time 9
+                      exact False.elim (exclude_0101001000 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 b hb h2 h10 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9)
+                    · -- branch 1 at time 9
+                      exact False.elim (exclude_0101001001 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 b hb h4 h9 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9)
+                  · -- branch 1 at time 8
+                    intro r9
+                    rcases r9 with r9 | r9
+                    · -- branch 0 at time 9
+                      intro r10
+                      rcases r10 with r10 | r10
+                      · -- branch 0 at time 10
+                        intro r11
+                        rcases r11 with r11 | r11
+                        · -- branch 0 at time 11
+                          exact False.elim (exclude_010100101000 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 b hb h4 h12 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11)
+                        · -- branch 1 at time 11
+                          intro r12
+                          rcases r12 with r12 | r12
+                          · -- branch 0 at time 12
+                            intro r13
+                            rcases r13 with r13 | r13
+                            · -- branch 0 at time 13
+                              exact False.elim (exclude_01010010100100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 b hb h9 h14 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13)
+                            · -- branch 1 at time 13
+                              exact False.elim (exclude_01010010100101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 b hb h1 h14 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13)
+                          · -- branch 1 at time 12
+                            exact False.elim (exclude_0101001010011 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 b hb r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12)
+                      · -- branch 1 at time 10
+                        exact False.elim (exclude_01010010101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 b hb h1 h11 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10)
+                    · -- branch 1 at time 9
+                      exact False.elim (exclude_0101001011 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 b hb r0 r1 r2 r3 r4 r5 r6 r7 r8 r9)
+                · -- branch 1 at time 7
+                  exact False.elim (exclude_01010011 x0 x1 x2 x3 x4 x5 x6 x7 x8 b hb r0 r1 r2 r3 r4 r5 r6 r7)
+            · -- branch 1 at time 5
+              exact False.elim (exclude_010101 x0 x1 x2 x3 x4 x5 x6 b hb h1 h6 r0 r1 r2 r3 r4 r5)
+          · -- branch 1 at time 4
+            exact False.elim (exclude_01011 x0 x1 x2 x3 x4 x5 b hb r0 r1 r2 r3 r4)
+      · -- branch 1 at time 2
+        exact False.elim (exclude_011 x0 x1 x2 x3 b hb r0 r1 r2)
+  · -- branch 1 at time 0
+    intro r1
+    rcases r1 with r1 | r1
+    · -- branch 0 at time 1
+      intro r2
+      rcases r2 with r2 | r2
+      · -- branch 0 at time 2
+        intro r3
+        rcases r3 with r3 | r3
+        · -- branch 0 at time 3
+          exact False.elim (exclude_1000 x0 x1 x2 x3 x4 b hb h1 h4 r0 r1 r2 r3)
+        · -- branch 1 at time 3
+          intro r4
+          rcases r4 with r4 | r4
+          · -- branch 0 at time 4
+            intro r5
+            rcases r5 with r5 | r5
+            · -- branch 0 at time 5
+              intro r6
+              rcases r6 with r6 | r6
+              · -- branch 0 at time 6
+                exact False.elim (exclude_1001000 x0 x1 x2 x3 x4 x5 x6 x7 b hb h1 h7 r0 r1 r2 r3 r4 r5 r6)
+              · -- branch 1 at time 6
+                exact False.elim (exclude_1001001 x0 x1 x2 x3 x4 x5 x6 x7 b hb h1 h6 r0 r1 r2 r3 r4 r5 r6)
+            · -- branch 1 at time 5
+              intro r6
+              rcases r6 with r6 | r6
+              · -- branch 0 at time 6
+                intro r7
+                rcases r7 with r7 | r7
+                · -- branch 0 at time 7
+                  intro r8
+                  rcases r8 with r8 | r8
+                  · -- branch 0 at time 8
+                    exact False.elim (exclude_100101000 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 b hb h1 h9 r0 r1 r2 r3 r4 r5 r6 r7 r8)
+                  · -- branch 1 at time 8
+                    intro r9
+                    rcases r9 with r9 | r9
+                    · -- branch 0 at time 9
+                      intro r10
+                      rcases r10 with r10 | r10
+                      · -- branch 0 at time 10
+                        exact False.elim (exclude_10010100100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 b hb h6 h11 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10)
+                      · -- branch 1 at time 10
+                        intro r11
+                        rcases r11 with r11 | r11
+                        · -- branch 0 at time 11
+                          intro r12
+                          rcases r12 with r12 | r12
+                          · -- branch 0 at time 12
+                            intro r13
+                            rcases r13 with r13 | r13
+                            · -- branch 0 at time 13
+                              exact False.elim (exclude_10010100101000 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 b hb h1 h14 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13)
+                            · -- branch 1 at time 13
+                              intro r14
+                              rcases r14 with r14 | r14
+                              · -- branch 0 at time 14
+                                intro r15
+                                rcases r15 with r15 | r15
+                                · -- branch 0 at time 15
+                                  exact False.elim (exclude_1001010010100100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 b hb h11 h16 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14 r15)
+                                · -- branch 1 at time 15
+                                  exact False.elim (exclude_1001010010100101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 b hb h3 h16 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14 r15)
+                              · -- branch 1 at time 14
+                                exact False.elim (exclude_100101001010011 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 b hb r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12 r13 r14)
+                          · -- branch 1 at time 12
+                            exact False.elim (exclude_1001010010101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 b hb h0 h13 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12)
+                        · -- branch 1 at time 11
+                          exact False.elim (exclude_100101001011 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 b hb r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11)
+                    · -- branch 1 at time 9
+                      exact False.elim (exclude_1001010011 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 b hb r0 r1 r2 r3 r4 r5 r6 r7 r8 r9)
+                · -- branch 1 at time 7
+                  exact False.elim (exclude_10010101 x0 x1 x2 x3 x4 x5 x6 x7 x8 b hb h3 h8 r0 r1 r2 r3 r4 r5 r6 r7)
+              · -- branch 1 at time 6
+                exact False.elim (exclude_1001011 x0 x1 x2 x3 x4 x5 x6 x7 b hb r0 r1 r2 r3 r4 r5 r6)
+          · -- branch 1 at time 4
+            exact False.elim (exclude_10011 x0 x1 x2 x3 x4 x5 b hb r0 r1 r2 r3 r4)
+      · -- branch 1 at time 2
+        intro r3
+        rcases r3 with r3 | r3
+        · -- branch 0 at time 3
+          intro r4
+          rcases r4 with r4 | r4
+          · -- branch 0 at time 4
+            intro r5
+            rcases r5 with r5 | r5
+            · -- branch 0 at time 5
+              exact False.elim (exclude_101000 x0 x1 x2 x3 x4 x5 x6 b hb h3 h6 r0 r1 r2 r3 r4 r5)
+            · -- branch 1 at time 5
+              intro r6
+              rcases r6 with r6 | r6
+              · -- branch 0 at time 6
+                intro r7
+                rcases r7 with r7 | r7
+                · -- branch 0 at time 7
+                  intro r8
+                  rcases r8 with r8 | r8
+                  · -- branch 0 at time 8
+                    exact False.elim (exclude_101001000 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 b hb h1 h9 r0 r1 r2 r3 r4 r5 r6 r7 r8)
+                  · -- branch 1 at time 8
+                    exact False.elim (exclude_101001001 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 b hb h3 h8 r0 r1 r2 r3 r4 r5 r6 r7 r8)
+                · -- branch 1 at time 7
+                  intro r8
+                  rcases r8 with r8 | r8
+                  · -- branch 0 at time 8
+                    intro r9
+                    rcases r9 with r9 | r9
+                    · -- branch 0 at time 9
+                      intro r10
+                      rcases r10 with r10 | r10
+                      · -- branch 0 at time 10
+                        exact False.elim (exclude_10100101000 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 b hb h3 h11 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10)
+                      · -- branch 1 at time 10
+                        intro r11
+                        rcases r11 with r11 | r11
+                        · -- branch 0 at time 11
+                          intro r12
+                          rcases r12 with r12 | r12
+                          · -- branch 0 at time 12
+                            exact False.elim (exclude_1010010100100 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 b hb h8 h13 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12)
+                          · -- branch 1 at time 12
+                            exact False.elim (exclude_1010010100101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 b hb h0 h13 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11 r12)
+                        · -- branch 1 at time 11
+                          exact False.elim (exclude_101001010011 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 b hb r0 r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 r11)
+                    · -- branch 1 at time 9
+                      exact False.elim (exclude_1010010101 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 b hb h0 h10 r0 r1 r2 r3 r4 r5 r6 r7 r8 r9)
+                  · -- branch 1 at time 8
+                    exact False.elim (exclude_101001011 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 b hb r0 r1 r2 r3 r4 r5 r6 r7 r8)
+              · -- branch 1 at time 6
+                exact False.elim (exclude_1010011 x0 x1 x2 x3 x4 x5 x6 x7 b hb r0 r1 r2 r3 r4 r5 r6)
+          · -- branch 1 at time 4
+            exact False.elim (exclude_10101 x0 x1 x2 x3 x4 x5 b hb h0 h5 r0 r1 r2 r3 r4)
+        · -- branch 1 at time 3
+          exact False.elim (exclude_1011 x0 x1 x2 x3 x4 b hb r0 r1 r2 r3)
+    · -- branch 1 at time 1
+      exact False.elim (exclude_11 x0 x1 x2 b hb r0 r1)
+
+end Collatz.Exploration.WiderBandArithmetic
diff --git a/Collatz/Exploration/WiderBandClock.lean b/Collatz/Exploration/WiderBandClock.lean
new file mode 100644
index 00000000..fbaf2315
--- /dev/null
+++ b/Collatz/Exploration/WiderBandClock.lean
@@ -0,0 +1,96 @@
+import Collatz.Exploration.FiveBandClock
+import Collatz.Exploration.BandClock
+import Collatz.Exploration.WiderBandArithmetic
+
+/-! A wider sharp band clock, keeping the descent/growth alternative explicit. -/
+namespace Collatz.Exploration.WiderBandClock
+open BarrierKernel BandClock
+
+/-- The inclusive ratio-21/4 band cannot contain eighteen sampled states. -/
+theorem no_band_seventeen {b n : Nat} (hb : 1 < b)
+    (hs : ∀ k, k ≤ 17 → b ≤ orbit k n ∧ 4*orbit k n ≤ 21*b) : False := by
+  have bounds0 := hs 0 (by decide)
+  have bounds1 := hs 1 (by decide)
+  have bounds2 := hs 2 (by decide)
+  have bounds3 := hs 3 (by decide)
+  have bounds4 := hs 4 (by decide)
+  have bounds5 := hs 5 (by decide)
+  have bounds6 := hs 6 (by decide)
+  have bounds7 := hs 7 (by decide)
+  have bounds8 := hs 8 (by decide)
+  have bounds9 := hs 9 (by decide)
+  have bounds10 := hs 10 (by decide)
+  have bounds11 := hs 11 (by decide)
+  have bounds12 := hs 12 (by decide)
+  have bounds13 := hs 13 (by decide)
+  have bounds14 := hs 14 (by decide)
+  have bounds15 := hs 15 (by decide)
+  have bounds16 := hs 16 (by decide)
+  have bounds17 := hs 17 (by decide)
+  have rel (k : Nat) (hk : k ≤ 16) :
+      (2*orbit (k+1) n = orbit k n ∧ (orbit k n)%2 = 0) ∨
+      (orbit (k+1) n = 3*orbit k n+1 ∧ (orbit k n)%2 = 1) := by
+    have hp : 0 < orbit k n := by have := hs k (by omega); omega
+    have h := FiveBandClock.step_relation hp
+    rw [← orbit_step_commute, ← orbit_succ_steps] at h
+    exact h
+  exact WiderBandArithmetic.impossible_trace b (orbit 0 n) (orbit 1 n) (orbit 2 n) (orbit 3 n) (orbit 4 n) (orbit 5 n) (orbit 6 n) (orbit 7 n) (orbit 8 n) (orbit 9 n) (orbit 10 n) (orbit 11 n) (orbit 12 n) (orbit 13 n) (orbit 14 n) (orbit 15 n) (orbit 16 n) (orbit 17 n) hb
+    bounds0 bounds1 bounds2 bounds3 bounds4 bounds5 bounds6 bounds7 bounds8 bounds9 bounds10 bounds11 bounds12 bounds13 bounds14 bounds15 bounds16 bounds17
+    (rel 0 (by decide)) (rel 1 (by decide)) (rel 2 (by decide)) (rel 3 (by decide)) (rel 4 (by decide)) (rel 5 (by decide)) (rel 6 (by decide)) (rel 7 (by decide)) (rel 8 (by decide)) (rel 9 (by decide)) (rel 10 (by decide)) (rel 11 (by decide)) (rel 12 (by decide)) (rel 13 (by decide)) (rel 14 (by decide)) (rel 15 (by decide)) (rel 16 (by decide))
+
+/-- A universal exit clock for all natural starts and all integer barriers b>1. -/
+theorem exit_seventeen : ExitClock 21 4 17 := by
+  intro b n hb
+  by_cases h : ∃ k, k ≤ 17 ∧ (orbit k n < b ∨ 21*b < 4*orbit k n)
+  · exact h
+  · exfalso
+    apply no_band_seventeen (n := n) hb
+    intro k hk
+    by_cases hl : orbit k n < b
+    · exact False.elim (h ⟨k,hk,Or.inl hl⟩)
+    · by_cases hu : 21*b < 4*orbit k n
+      · exact False.elim (h ⟨k,hk,Or.inr hu⟩)
+      · omega
+
+theorem rejection_seventeen {b n : Nat} (hb : 1 < b) :
+    intervalCheck b (21*b/4) 17 n = false := by
+  by_cases ht : intervalCheck b (21*b/4) 17 n = true
+  · exfalso
+    have hs := (intervalCheck_iff b (21*b/4) 17 n).mp ht
+    apply no_band_seventeen (n := n) hb
+    intro k hk
+    have := hs k hk
+    omega
+  · cases he : intervalCheck b (21*b/4) 17 n <;> simp_all
+
+/-- One trace witnesses sharpness both at ratio 21/4 and at ratio 51/10. -/
+theorem clock_sharpness :
+    intervalCheck 379 (21*379/4) 16 1010 = true ∧
+    intervalCheck 379 (51*379/10) 16 1010 = true ∧ orbit 17 1010 = 361 := by decide
+
+theorem exit_fifty_one_tenths : ExitClock 51 10 17 := by
+  intro b n hb
+  obtain ⟨k,hk,hl | hu⟩ := exit_seventeen b n hb
+  · exact ⟨k,hk,Or.inl hl⟩
+  · exact ⟨k,hk,Or.inr (by omega)⟩
+
+theorem no_clock_sixteen : ¬ ExitClock 21 4 16 := by
+  intro h
+  have hc := (intervalCheck_iff 379 (21*379/4) 16 1010).mp clock_sharpness.1
+  exact no_band_through (b := 379) (n := 1010) h (by decide) (fun k hk => by have := hc k hk; omega)
+
+/-- Hypothetical lower-surviving orbits have a high visit in every 18-point window. -/
+theorem high_window {b n : Nat} (hb : 1 < b) (h : Kernel b n) (t : Nat) :
+    ∃ s, t ≤ s ∧ s ≤ t+17 ∧ 21*b < 4*orbit s n :=
+  BandClock.high_window exit_seventeen hb h t
+
+theorem finite_survival_witnesses {b n : Nat} (hb : 1 < b) (N : Nat)
+    (h : Survives b (18*N-1) n) :
+    ∃ f : Fin N → Nat,
+      (∀ q, f q < 18*N ∧ 21*b < 4*orbit (f q) n) ∧
+      (∀ a c, f a = f c → a = c) :=
+  BandClock.finite_survival_witnesses exit_seventeen hb N h
+
+theorem anchor_one_control : intervalCheck 1 (21/4) 100 1 = true := by decide
+
+end Collatz.Exploration.WiderBandClock
diff --git a/README.md b/README.md
index 150d4e4e..808da699 100644
--- a/README.md
+++ b/README.md
@@ -35,6 +35,9 @@ own verification instructions.
   a hypothetical orbit floor to exceed five times its starting value. Every
   arbitrary-start orbit exits `[b,5b]` within twelve steps for `b>1`; the
   clock is sharp and yields conditional high-visit witnesses.
+- [Sharp wider-band clock](Research/WiderBandClock.md) — the ratio-21/4
+  band has a sharp seventeen-step exit clock, with reusable finite witness
+  transfer for lower-surviving prefixes.
 - [Rational band obstruction](Research/RationalBandObstruction.md) — a
   denominator-aware cycle certificate, exact closure classification, and
   why the integer floor bound does not extend to rational floors.
diff --git a/Research/WiderBandClock.md b/Research/WiderBandClock.md
new file mode 100644
index 00000000..8ff5dd08
--- /dev/null
+++ b/Research/WiderBandClock.md
@@ -0,0 +1,103 @@
+# Sharp ratio-21/4 band clock
+
+For the ordinary integer Collatz map `C`, Lean now proves
+
+`∀ b>1, ∀ n, ∃ k≤17, C^k(n)<b ∨ 21b<4C^k(n)`.
+
+Thus every orbit exits the inclusive band `[b,21b/4]` by time seventeen.
+The same sharp clock holds for the narrower band `[b,51b/10]`. Bounds are
+cross-multiplied exact integer comparisons, including nonintegral upper
+endpoints. The executable checker uses `floor(21b/4)`.
+
+## Sharpness and comparison
+
+At `b=379`, the trajectory from 1010 is
+
+`1010→505→1516→758→379→1138→569→1708→854→427→1282→641→1924→962→481→1444→722→361`.
+
+Times zero through sixteen stay in both bands; time seventeen exits
+below the barrier. Lean verifies the trace endpoints and both successful
+sixteen-step checks. It also proves that the ratio-21/4 clock cannot be
+shortened to sixteen. The maximum before exit is 1924, less than both
+upper endpoints. This is a downward exit, so retaining the growth
+alternative is necessary.
+
+The earlier ratio-five result gives the shorter sharp clock twelve.
+These two results offer different threshold/horizon tradeoffs: the new
+one forces a larger conditional excursion at a longer horizon.
+The rational cycle in [the denominator obstruction note](RationalBandObstruction.md)
+shows why ignoring integrality can obstruct a wider-band proof.
+It does not contradict the theorem here, whose states and anchor are natural numbers.
+
+## Congruence-aware finite proof
+
+A branch word records even halvings (`0`) and odd updates (`1`). Its affine
+state equations have the form
+
+`D_i*x_i=A_i*x_0+C_i`,
+
+with `D_i` a power of two and `A_i` odd. At each next parity condition,
+the guide updates the source residue modulo `2D_i`, retaining compatibility
+with the previously known residue. It also intersects the exact rational
+inequalities `x_i≥2` and `4x_i≤21x_j` over all sampled states. The latter
+conditions test whether some fixed integer barrier can contain the trace:
+for an actual integer trace, the largest possible barrier is its minimum.
+A candidate source must lie in that interval and its residue class.
+
+The exact guide exhausts the tree at depth seventeen: 151 nodes and
+76 terminal branches. These numbers describe a finite certificate,
+not 76 separate mathematical discoveries. The generator is reproducible
+and supplies no trusted proof oracle.
+
+The Lean certificate proves 123 source-and-trace lemmas. Each states
+`∃q≥0, x_i=a_i*q+c_i` for every sampled state of its branch. A parent lemma,
+the next division-free transition, and a parity condition modulo two
+prove the next one. Each terminal branch is then contradicted by its
+parameterization and a small subset of interval bounds, or by incompatible
+parity. Earlier parity hypotheses are cleared after the parameterization
+absorbs them, keeping the arithmetic solver's context small. A final
+case-split theorem combines all terminal certificates. This is an exact
+finite analysis of the actual integer map, with no imported verified
+convergence range.
+
+Affine parity-word arithmetic is standard; the [rational obstruction
+note](RationalBandObstruction.md) links the primary literature and explains
+its cycle fixed-point formula. This investigation has not established
+literature priority for the specific sharp clock.
+
+## Reusable finite-prefix transfer
+
+`BandClock.ExitClock(P,Q,K)` abstracts the two-direction exit statement
+at the rational threshold `P/Q`. From any proved clock, the generic
+transfer theorem supplies an injective witness function
+
+`f : Fin N → Nat`, with `f(q)<(K+1)N` and `Pb<Q*C^(f(q))(n)`.
+
+It only needs lower survival through time `(K+1)N−1`. The proof selects
+one high time in each disjoint `(K+1)`-point block. The wrapper for the
+new clock gives `N` distinct high times below `18N` from survival through
+`18N−1`. A global fixed-barrier kernel gives a high visit in every
+18-point window. This is a conditional count statement at a fixed
+threshold; it neither constructs a nonconvergent orbit nor proves its
+values unbounded. The downward-or-growth alternative alone does not
+establish universal descent.
+
+## Verification
+
+Run `python3 scripts/audit_wider_band_clock.py`. It reproduces the
+source generator, builds all three new Lean modules, scans their sources
+for proof escapes, audits 214 named theorem axiom footprints (200 arithmetic
+certificate components, five generic transfers, nine clock results),
+and requires rejection of four false claims.
+
+Independent scalar tests check 1,298,909 exhaustive exits across both
+bands, 120,000 large-integer exits, 744 exact parametric prefix samples,
+133,637 lower-surviving windows, and 9,026 distinct block witnesses.
+They verify the sharp witness and controls for the excluded anchor one,
+loss of lower survival, and the different `3n−1` map. The maximum observed
+exit is seventeen. Finite tests corroborate the universal Lean proofs.
+
+The modules are exported by the library and the audit is included in CI.
+The conjecture and the requested frontier-innovative proportion remain
+unverified. Further work can examine wider ratios, additional source
+congruences, and how excursion witnesses interact with descent obligations.
diff --git a/scripts/audit_wider_band_clock.py b/scripts/audit_wider_band_clock.py
new file mode 100644
index 00000000..c09d5c03
--- /dev/null
+++ b/scripts/audit_wider_band_clock.py
@@ -0,0 +1,33 @@
+#!/usr/bin/env python3
+"""Reproduce and audit sharp seventeen-step clocks and generic witness transfer."""
+import subprocess
+from audit_barrier_kernel import ROOT, check_axioms, check_false_certificates
+from check_proof_escapes import violations
+
+MODULES = ['BandClock', 'WiderBandArithmetic', 'WiderBandClock']
+PREFIX = 'Collatz.Exploration.'
+
+
+def main():
+    subprocess.run(['python3', str(ROOT / 'scripts/generate_wider_band_arithmetic.py')],
+                   cwd=ROOT, check=True)
+    for name in MODULES:
+        assert not violations((ROOT / f'Collatz/Exploration/{name}.lean').read_text())
+    subprocess.run(['lake', 'build', PREFIX+'WiderBandClock'], cwd=ROOT, check=True)
+    subprocess.run(['python3', str(ROOT / 'scripts/test_wider_band_clock.py')],
+                   cwd=ROOT, check=True)
+    count = sum(check_axioms(ROOT / f'Collatz/Exploration/{name}.lean', PREFIX+name)
+                for name in MODULES)
+    barrier = PREFIX+'BarrierKernel.intervalCheck'
+    claims = [
+        f'example : {barrier} 379 (21*379/4) 16 1010 = false := by decide\n',
+        'example : Collatz.orbit 17 1010 = 362 := by decide\n',
+        f'example : {barrier} 1 (21/4) 17 1 = false := by decide\n',
+        'example : (List.range 18).any (fun k => decide (21*2 < 4*Collatz.orbit k 2)) = true := by decide\n',
+    ]
+    rejected = check_false_certificates(PREFIX+'WiderBandClock', claims)
+    print(f'{count} theorem axiom footprints checked; {rejected} false claims rejected')
+
+
+if __name__ == '__main__':
+    main()
diff --git a/scripts/generate_wider_band_arithmetic.py b/scripts/generate_wider_band_arithmetic.py
new file mode 100644
index 00000000..b8692af4
--- /dev/null
+++ b/scripts/generate_wider_band_arithmetic.py
@@ -0,0 +1,179 @@
+#!/usr/bin/env python3
+"""Exact congruence-aware branch guide; Lean checks every parametric trace and leaf."""
+import argparse
+from fractions import Fraction as F
+from itertools import combinations
+from math import ceil
+from pathlib import Path
+
+ROOT = Path(__file__).resolve().parents[1]
+SOURCE = ROOT / 'Collatz/Exploration/WiderBandArithmetic.lean'
+P, Q, HORIZON = 21, 4, 17
+
+
+def domain(states, residue, modulus):
+    low, high = F(0), None
+    for a, c, d in states:
+        low = max(low, F(2*d-c, a))
+    for a, c, d in states:
+        for e, f, g in states:
+            coefficient, rhs = Q*a*g-P*e*d, P*f*d-Q*c*g
+            if coefficient > 0:
+                limit = F(rhs, coefficient)
+                high = limit if high is None else min(high, limit)
+            elif coefficient < 0:
+                low = max(low, F(rhs, coefficient))
+            elif rhs < 0:
+                return None
+    first = residue+modulus*ceil((low-residue)/modulus)
+    return (low, high, first) if high is None or first <= high else None
+
+
+def tree():
+    nodes = {}
+    def walk(word, states, residue, modulus, valid=True):
+        node = dict(states=states, residue=residue, modulus=modulus, valid=valid)
+        nodes[word] = node
+        if not valid:
+            node['terminal'] = True
+            return
+        if not domain(states, residue, modulus):
+            node['terminal'] = True
+            node['core'] = next(indices for size in range(1, len(states)+1)
+                                for indices in combinations(range(len(states)), size)
+                                if not domain([states[i] for i in indices], residue, modulus))
+            return
+        if len(word) == HORIZON:
+            raise AssertionError(('unexcluded branch', word, node))
+        node['terminal'] = False
+        a, c, d = states[-1]
+        for bit in (0, 1):
+            new_modulus = 2*d
+            new_residue = (pow(a, -1, new_modulus)*(bit*d-c)) % new_modulus
+            compatible = (residue-new_residue) % min(modulus, new_modulus) == 0
+            nr, nm = (new_residue, new_modulus) if new_modulus > modulus else (residue, modulus)
+            state = (a, c, 2*d) if bit == 0 else (3*a, 3*c+d, d)
+            walk(word+str(bit), states+[state], nr, nm, compatible)
+    walk('', [(1, 0, 1)], 0, 1)
+    return nodes
+
+
+def relation(k, bit=None):
+    even = f'(2*x{k+1} = x{k} ∧ x{k}%2 = 0)'
+    odd = f'(x{k+1} = 3*x{k}+1 ∧ x{k}%2 = 1)'
+    return even+' ∨ '+odd if bit is None else (even if bit == '0' else odd)
+
+
+def parameters(node):
+    r, m = node['residue'], node['modulus']
+    result = []
+    for a, c, d in node['states']:
+        assert a*m % d == (a*r+c) % d == 0
+        result.append((a*m//d, (a*r+c)//d))
+    return result
+
+
+def header(name, word, bounds=None):
+    depth = len(word)
+    out = [f'theorem {name}',
+           '    ('+' '.join(f'x{i}' for i in range(depth+1))+' : Nat)']
+    if bounds is not None:
+        out += ['    (b : Nat) (hb : 1 < b)']
+        out += [f'    (h{i} : b ≤ x{i} ∧ {Q}*x{i} ≤ {P}*b)' for i in bounds]
+    out += [f'    (r{i} : {relation(i, word[i])})' for i in range(depth)]
+    return '\n'.join(out)+'\n'
+
+
+def certificate():
+    nodes = tree()
+    out = ['import Collatz.Basic\n\n',
+           '/-! Generated residue-and-affine certificates for the inclusive ratio-21/4 band.\n',
+           'Every branch and arithmetic conclusion is independently checked by Lean. -/\n',
+           'namespace Collatz.Exploration.WiderBandArithmetic\n\n',
+           'set_option maxHeartbeats 2000000\n',
+           'set_option linter.unusedVariables false\n\n']
+    # Prefix lemmas are emitted in increasing length, so parent proofs are available.
+    for word in sorted(nodes, key=lambda w: (len(w), w)):
+        if not word or not nodes[word]['valid']:
+            continue
+        node, parent = nodes[word], nodes[word[:-1]]
+        depth = len(word)
+        ps = parameters(node)
+        out += [f'/-- Exact source residue and full affine trace for branch `{word}`. -/\n',
+                header('parameters_'+word, word),
+                '    : ∃ q : Nat, '+' ∧ '.join(f'x{i} = {a}*q+{c}' for i,(a,c) in enumerate(ps))+' := by\n']
+        if depth == 1:
+            out += ['  let q := x0\n', '  have p0 : x0 = q := rfl\n']
+        else:
+            args = ' '.join([f'x{i}' for i in range(depth)]+[f'r{i}' for i in range(depth-1)])
+            binders = ','.join(['q']+[f'p{i}' for i in range(depth)])
+            out += [f'  obtain ⟨{binders}⟩ := parameters_{word[:-1]} {args}\n']
+        out += [f'  have hstep := r{depth-1}.1\n', f'  have hparity := r{depth-1}.2\n',
+                '  clear '+' '.join(f'r{i}' for i in range(depth))+'\n']
+        if node['modulus'] > parent['modulus']:
+            epsilon = (node['residue']-parent['residue'])//parent['modulus']
+            assert epsilon in (0,1)
+            out += [f'  have hq : q = 2*(q/2)+{epsilon} := by omega\n']
+            witness = 'q/2'
+        else:
+            witness = 'q'
+        out += ['  clear hparity\n']
+        out += ['  refine ⟨'+witness+','+','.join('?_' for _ in range(depth+1))+'⟩ <;> omega\n\n']
+    leaves = [w for w,n in nodes.items() if n['terminal']]
+    for word in leaves:
+        node = nodes[word]
+        depth = len(word)
+        core = node.get('core', [])
+        out += [f'/-- Terminal branch `{word}` cannot satisfy the band bounds. -/\n',
+                header('exclude_'+word, word, core), '    : False := by\n']
+        if node['valid']:
+            args = ' '.join([f'x{i}' for i in range(depth+1)]+[f'r{i}' for i in range(depth)])
+            binders = ','.join(['q']+[f'p{i}' for i in range(depth+1)])
+            out += [f'  obtain ⟨{binders}⟩ := parameters_{word} {args}\n',
+                    '  clear '+' '.join(f'r{i}' for i in range(depth))+'\n', '  omega\n\n']
+        else:
+            args = ' '.join([f'x{i}' for i in range(depth)]+[f'r{i}' for i in range(depth-1)])
+            binders = ','.join(['q']+[f'p{i}' for i in range(depth)])
+            out += [f'  obtain ⟨{binders}⟩ := parameters_{word[:-1]} {args}\n',
+                    f'  have hparity := r{depth-1}.2\n',
+                    '  clear '+' '.join(f'r{i}' for i in range(depth))+'\n', '  omega\n\n']
+    out += ['theorem impossible_trace\n',
+            '    (b '+' '.join(f'x{i}' for i in range(HORIZON+1))+' : Nat) (hb : 1 < b)\n']
+    out += [f'    (h{i} : b ≤ x{i} ∧ {Q}*x{i} ≤ {P}*b)\n' for i in range(HORIZON+1)]
+    out += [f'    (r{i} : {relation(i)})\n' for i in range(HORIZON)]
+    out += ['    : False := by\n', '  revert '+' '.join(f'r{i}' for i in range(HORIZON-1,-1,-1))+'\n']
+    def emit(word, indent):
+        node = nodes[word]
+        if node['terminal']:
+            depth = len(word)
+            args = [f'x{i}' for i in range(depth+1)]+['b','hb']+[
+                f'h{i}' for i in node.get('core',[])]+[f'r{i}' for i in range(depth)]
+            out.append(' '*indent+'exact False.elim (exclude_'+word+' '+' '.join(args)+')\n')
+            return
+        k = len(word)
+        out.append(' '*indent+f'intro r{k}\n')
+        out.append(' '*indent+f'rcases r{k} with r{k} | r{k}\n')
+        for bit in (0,1):
+            out.append(' '*indent+f'· -- branch {bit} at time {k}\n')
+            emit(word+str(bit), indent+2)
+    emit('', 2)
+    out += ['\nend Collatz.Exploration.WiderBandArithmetic\n']
+    assert len(leaves) == 76 and max(map(len, leaves)) == HORIZON
+    assert sum(F(1,2**len(w)) for w in leaves) == 1
+    return ''.join(out), nodes
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--write', action='store_true')
+    args = parser.parse_args()
+    expected, nodes = certificate()
+    if args.write:
+        SOURCE.write_text(expected)
+    else:
+        assert SOURCE.read_text() == expected, 'Generated certificate differs'
+    print(f'{len(nodes)} tree nodes; 76 terminal branches; maximum depth {HORIZON}; source reproduced')
+
+
+if __name__ == '__main__':
+    main()
diff --git a/scripts/test_wider_band_clock.py b/scripts/test_wider_band_clock.py
new file mode 100644
index 00000000..9e6c8973
--- /dev/null
+++ b/scripts/test_wider_band_clock.py
@@ -0,0 +1,77 @@
+#!/usr/bin/env python3
+"""Direct rational-band exits, parametric prefixes, and finite high-visit witnesses."""
+import random
+from test_barrier_kernel import trajectory
+from generate_wider_band_arithmetic import tree, parameters
+
+
+def exit_time(P, Q, b, start):
+    n = start
+    for k in range(18):
+        if n < b or P*b < Q*n:
+            return k
+        n = n//2 if n % 2 == 0 else 3*n+1
+    raise AssertionError((P, Q, b, start, 'accepted seventeen-step band'))
+
+
+def main():
+    exhaustive = large = windows = blocks = prefixes = 0
+    maximum = 0
+    for P, Q in [(21,4), (51,10)]:
+        for b in range(2, 501):
+            for n in range(P*b//Q+3):
+                k = exit_time(P,Q,b,n)
+                maximum = max(maximum,k)
+                exhaustive += 1
+        rng = random.Random(P*100+Q)
+        for _ in range(10000):
+            b = rng.randrange(2,10**120)
+            for n in [0,b,2*b,P*b//Q,P*b//Q+1,rng.randrange(b,P*b//Q+1)]:
+                maximum = max(maximum,exit_time(P,Q,b,n))
+                large += 1
+    assert maximum == 17
+    sharp = trajectory(1010,17)
+    assert sharp == [1010,505,1516,758,379,1138,569,1708,854,427,1282,
+                     641,1924,962,481,1444,722,361]
+    for P,Q in [(21,4),(51,10)]:
+        assert all(379 <= n and Q*n <= P*379 for n in sharp[:-1])
+        assert exit_time(P,Q,379,1010) == 17
+    nodes = tree()
+    for word,node in nodes.items():
+        if not node['valid']:
+            continue
+        ps = parameters(node)
+        for q in [0,1,2,17,65537,2**180-1]:
+            values = [a*q+c for a,c in ps]
+            for bit,n,m in zip(word,values,values[1:]):
+                assert n%2 == int(bit)
+                assert m == (n//2 if bit=='0' else 3*n+1)
+            prefixes += 1
+    for seed in list(range(2,2002))+[2**90-1,2**180-1]:
+        values = trajectory(seed,511)
+        for b in sorted({2,max(2,seed//5),max(2,seed//2),seed}):
+            end = next((i for i,n in enumerate(values) if n<b),len(values))
+            prefix = values[:end]
+            for t in range(max(0,len(prefix)-17)):
+                assert any(21*b<4*n for n in prefix[t:t+18])
+                windows += 1
+            witnesses = []
+            for q in range(len(prefix)//18):
+                s = next(i for i in range(18*q,18*q+18) if 21*b<4*prefix[i])
+                witnesses.append(s)
+                blocks += 1
+            assert len(set(witnesses)) == len(witnesses)
+    assert all(1 <= n and 4*n <= 21 for n in trajectory(1,100))
+    # Changing the sign gives a trapped cycle at barrier 5.
+    n = 5
+    for _ in range(100):
+        assert 5 <= n and 4*n <= 21*5
+        n = n//2 if n%2==0 else 3*n-1
+    assert 4*max(trajectory(2,17)) <= 21*2  # lower survival is essential
+    print(f'{exhaustive} exhaustive and {large} large-integer band exits; maximum 17; '
+          f'{prefixes} affine prefix samples; {windows} lower-surviving windows; '
+          f'{blocks} distinct block witnesses; sharpness and hypothesis controls passed')
+
+
+if __name__ == '__main__':
+    main()