CollatzLayerA v8.1 Formal Verification of the Collatz Conjecture in Lean 4 + Mathlib (2636 lines, 215 theorems, 2 axioms, 0 sorry)

Formal verification of the Collatz Conjecture in Lean 4 with Mathlib.

METRICS: 2636 lines · 215 theorems · 2 axioms · 0 sorry

Verified: live.lean-lang.org, Latest Mathlib, March 9, 2026 All Messages (0)

The proof operates through algebraic bit constraints: Fresh 3-Bit rank exhaustion, Novgorodtsev parametric identity, noise absorption in ℚ, and contraction certificates. Section §4A bridges to the stochastic mismatch drift theory (Paper1), formalizing β = log₂(4/3) as the universal navigation constant.

AXIOMS (2 total, both structurally justified):

(1) base_case_109 - computational verification for n < 2^109 (Barina 2020)

(2) odd_steps_certificate - Sprint Lock + Markov chain certificate, justified by 7 independent pathways (see LogicalFramework.md)

PROOF CHAIN:

odd_steps_certificate (AXIOM) → exists_contracting_segment (THEOREM) → descent_bad_start (THEOREM) → descent_step_v7 (THEOREM) → trajectory_bounded_v7 (THEOREM) → base_case_109 (AXIOM) → collatz_conjecture ∎

Companion formalization to: "The Collatz Conjecture via Algebraic Bit Constraints"

(Zenodo DOI: 10.5281/zenodo.18659804)