{"rewrite":{"id":"r_91dc65c2c7308dee71ded99c","clusterId":"c_7c0c4bd5fb8a6dd3f54a0522","slug":"ai-assisted-collatz-disproof-invalidated-by-lean-kernel-bug","model":"deepseek-v4-flash:free","headline":"AI-Assisted Collatz Disproof Invalidated by Lean Kernel Bug","summary":"A project claiming to disprove the Collatz conjecture with AI assistance was accepted by the theorem prover Lean, but the proof exploited a bug in Lean's kernel. Lean developer Leonardo de Moura published a postmortem explaining the proof is invalid. The bug allowed the kernel to accept the proposition False, meaning any conclusion could be derived. The issue was reported on July 28 and involved nested inductive types and phantom type parameters.","whyItMatters":"The incident shows that even a trusted proof assistant like Lean can be fooled by crafted declarations that exploit kernel bugs, undermining the reliability of AI-assisted formal proofs.","webCardHtml":"\u003cp\u003eRaman Kumar, a formal verification specialist, published a GitHub project on July 25 claiming to have disproved the Collatz conjecture with AI assistance. The project did not present a specific counterexample but asserted in Lean that a number exists which never reaches 1.\u003c/p\u003e\u003cp\u003eLean\u0026#39;s design routes user code through an elaborator and then a kernel that checks type consistency. The project avoided the \u0026#39;sorry\u0026#39; placeholder and extra axioms, appearing to be a valid formal proof. However, Kumar found that Lean could be made to accept the proposition False, which is unrelated to the Collatz conjecture.\u003c/p\u003e\u003cp\u003eResearcher Kiran Gopinathan condensed the issue into a small reproduction and reported it to the Lean team on July 28. The bug lay in the kernel\u0026#39;s handling of nested inductive types, where phantom type parameters were omitted from auxiliary types, allowing mismatched arguments to evade checks. Exploiting it required metaprogramming to send crafted declarations directly to the kernel.\u003c/p\u003e","blueskyPost":"Lean's kernel bug let the prover accept False, so the Collatz disproof collapses. The postmortem from Leonardo de Moura is the real artifact.","twitterPost":"Lean's kernel bug let the prover accept False, invalidating the Collatz disproof. Leonardo de Moura's postmortem is the real takeaway.","threadsPost":"The Collatz disproof fell to a bug in Lean's kernel, which accepted the proposition False. That means any conclusion could be derived, so the proof is void. Leonardo de Moura's postmortem explains the flaw, which involved nested inductive types and phantom parameters.","newsletterBlurb":"A project claiming to disprove the Collatz conjecture with AI assistance was accepted by Lean, but it exploited a kernel bug. The bug allowed the kernel to accept the proposition False, meaning the proof is invalid. Lean developer Leonardo de Moura published a postmortem explaining the issue.","attributionJson":"[{\"source\":\"GIGAZINE\",\"url\":\"https://gigazine.net/news/20260803-collatz-lean-kernel-bug/\",\"title\":\"AI-Assisted 'Disproof of Collatz Conjecture' Invalidated, Found to Exploit Lean Kernel Bug\"}]","lintFlagsJson":null,"lintHits":0,"costUsd":0,"inputTokens":4648,"outputTokens":603,"status":"published","repairAttempts":0,"nextRepairAt":null,"factsAttemptedAt":1786310758,"createdAt":"2026-08-09T21:00:43.000Z","publishedAt":"2026-08-09T21:01:44.000Z","updatedAt":"2026-08-09T21:00:43.000Z"},"cluster":{"id":"c_7c0c4bd5fb8a6dd3f54a0522","canonicalTitle":"AI支援で作られた「コラッツ予想の反証」は無効、Leanのカーネルバグを突いていたことが判明","representativeArticleId":"a_d813ecbb74a787e14becee53","sourceCount":1,"writtenSourceCount":1,"writeAttempts":1,"isSolo":true,"entitiesJson":"{\"anime_titles\":[],\"manga_titles\":[],\"work_titles\":[],\"studios\":[],\"people\":[\"Leonardo de Moura\"],\"type\":\"news\",\"domain\":\"other\",\"is_roundup\":false}","contentType":"news","status":"published","firstSeenAt":"2026-08-03T12:00:00.000Z","lastSeenAt":"2026-08-03T12:00:00.000Z","updatedAt":"2026-08-09T21:01:44.000Z"},"attribution":[{"source":"GIGAZINE","url":"https://gigazine.net/news/20260803-collatz-lean-kernel-bug/","title":"AI支援で作られた「コラッツ予想の反証」は無効、Leanのカーネルバグを突いていたことが判明"}],"entities":{"anime_titles":[],"manga_titles":[],"work_titles":[],"studios":[],"people":["Leonardo de Moura"],"type":"news","domain":"other","is_roundup":false},"keyFacts":null}