Formal exploration of the Collatz conjecture in Lean, with verified partial results, computational experiments, and literature notes. The conjecture remains unproved.
The main library uses Lean core. A separate Mathlib extension contains additional analytic results and verification instructions.
Install elan, then run:
lake build CollatzThe Lean version is pinned in lean-toolchain. Run the integrity checks
(requires Bash and Python 3):
bash scripts/check_integrity.shCI also checks generated certificates and the exact interval and coefficient-descent developments. The Mathlib extension has its own verification instructions.
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First passage through 2,592 steps — a stronger conditional descent theorem, an exact residual condition equivalent to Collatz, and 32,768 new depth-fifteen class certificates.
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Stopping atlas and first crossing through 1,538 steps — 15,360 infinite-class certificates, finite counting conservation, a tighter discrepancy bound, and explicit remaining universal-descent obligations.
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Research status — results, open questions, and limitations.
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Proof index — guide to the Lean library.
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First coefficient crossing through 1,024 steps — a conditional descent theorem for unbounded inputs, retained from the universal-descent development; it does not assert a crossing by 1,024 for every input.
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Coefficient crossing and interval shape — effective finite-exception transfer, a separately certified 256-step theorem, and the exact interval-shape consequences.
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Exact first-descent intervals — complete classifier, refinement conservation, and the remaining coverage obligation.
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Natural stopping density, Korec density bounds, and inverse interval decisions.
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Research notes and argument summaries — experiments and verification records.
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Literature — sources and references.
Conditional theorems keep their hypotheses explicit. Finite computations and almost-everywhere results do not prove convergence for every positive input.