AWESOME AI PROOFS
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Research / Aug 1, 2026

Collatz: an invalid machine-checked disproof

Does repeatedly halving an even integer, or replacing an odd integer by 3n + 1, always eventually reach 1?

Model / AI: Not specified

debunked

Problem explanation →

Aug 1, 2026

The Collatz kernel-soundness episode

Model / AI: Not specified

debunked

an AI-assisted sorry-free Lean "disproof" of Collatz stood for about three days, 25 to 28 July, by exploiting a phantom-parameter bug in the kernel's nested inductive types, and cleared the independent Nanoda checker by hitting a second, separate bug; Kiran Gopinathan reduced it to a proof of False and the Lean team patched it within an hour.

Source read 2026-09-08. Read the Lean maintainer’s postmortem describing the kernel bug and the separate outdated-nanoda bug. No checker was rerun.