OpenAI Claims ETH False, Publishes Lean Proof

If the claim survives scrutiny, it would reshape theoretical computer science—but it remains an extraordinary, independently unverified result rather than settled fact.

• –The claimed bound is subexponential, not polynomial, so it refutes ETH without resolving P versus NP.
• –ETH supports hundreds of conditional lower bounds across graph algorithms, databases, geometry, and computational biology.
• –Lean checks formal derivations, but reviewers must verify that the formal statement and complexity model faithfully capture standard ETH.
• –No immediate practical speedup follows; translating the asymptotic result into useful algorithms will require substantial work.
• –The public artifacts and expert-led review make this a significant test of AI-generated research verification.