Updates
What changed in OpenAI’s math release and in the claims we follow: new results, revised and withdrawn papers, new Lean proofs, and claims announced outside the catalogue. Newest first, back to the first release.
Follow with RSS. Last updated October 27, 2026.
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Beyond OpenAI’s catalogue, four more: AX02, a zero-free half-plane Re s > 31/32 for every Dedekind zeta function (Cureton and Thorner, with AxiomProver), building on 003 and 029; AX03, the Huang–Jiang–Oblomkov conjecture (Huang, Lau and Ono); AX04, an explicit positive density for Collatz, not a proof of the conjecture (Lau); and AN02, more than two thirds of the zeta zeros simple and on the critical line, first found by Claude. AI Proved What? is made with Claude, Anthropic’s AI; Anthropic’s own results are held to the same standards as every other lab’s, using only public sources. Beyond OpenAI
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Beyond OpenAI’s catalogue: new episodes on results from other labs: AX01, Axiom Math’s Lean proof of the classification of finite simple groups; PSI01–05, five results by PSI on Open Quantum Problems; and AN01, Anthropic’s Lean proof of Fermat’s Last Theorem. AI Proved What? is made with Claude, Anthropic’s AI; Anthropic’s own results are held to the same standards as every other lab’s, using only public sources. Beyond OpenAI
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New episode for 079: local smoothing for the wave equation in every dimension, OpenAI’s October 25 paper, with its consequences and its Lean proof. It replaces the three-dimensional episode, which stays listed under Versions. Episode out
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New result 378: OpenAI claims the Exponential Time Hypothesis is false, with a deterministic algorithm that counts satisfying assignments of k-CNF formulas in subexponential time and polynomial space, and a Lean proof. OpenAI says an independent working group of computer scientists led by Russell Impagliazzo, Ramamohan Paturi and Ryan Williams will examine and explain the proof. Episode out
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Result 079 extended to every dimension: a new paper, dated October 25, proves Sogge’s local smoothing conjecture for the wave equation in every spatial dimension n ≥ 2, with a Lean proof. OpenAI says it also yields the Kakeya maximal and dimension conjectures and Stein’s spherical restriction estimates. By our reading it implies the claims of 074 and 078 and the sphere and paraboloid cases of 077. Its new episode is out. Revised
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Lean proof added for 032, the rational Hodge conjecture for CM abelian varieties. Its scope notes leave out the consequences for the Tate and Hodge standard conjectures. Lean
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Code restored for 266: OpenAI restored the C++ source and saved numerical records for the computation that excludes a fourth mutually unbiased basis in dimension six, with a Python checker.
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Three papers withdrawn after a sign error in “Algebraicity of Weil classes on split abelian eightfolds” and two papers that depend on it; 14 other manuscripts revised and 6 Lean formalizations added. The catalogue now holds 719 manuscripts in 372 results. Withdrawn
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OpenAI’s math release: github.com/openai/math opens with 722 manuscripts in 372 result families.
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Announced outside the math release: finite-time blowup for Navier–Stokes and Euler, two papers with Lean proofs in openai/NavierStokesAndEuler. Special