OpenAI withdraws three math manuscripts after a sign error

OpenAI says a sign error in one manuscript undermined both that paper’s argument and a construction used by two papers that depended on it. The three withdrawn titles are “Algebraicity of Weil classes on split abelian eightfolds,” “Algebraicity of Kuga–Satake Correspondences for K3 Surfaces,” and “The rational Hodge conjecture for products of K3 surfaces.”[1] The repository now includes notices explaining the gap and linking to archived versions of the manuscripts.[1] Those notices provide readers with a route to the earlier texts while identifying the reason for the withdrawals.[1]

The three withdrawals were not the only changes. OpenAI says it revised 14 other manuscripts, making proof repairs, correcting statements, clarifying hypotheses and dependencies, and correcting a citation.[1] It also updated 13 additional manuscripts to cite revised editions of companion papers.[1] The repository update included six formalizations and five other additions covering supporting results; a separate account described six new Lean formalizations, 19 modifications, and three withdrawals.[1][2] For readers following a specific result, the changed manuscripts and their dependencies may matter as much as the three withdrawals.

An OpenAI spokesperson said the company identified the errors during an audit.[3] OpenAI says the work came from an internal frontier model and that its shared Lean formalizations allow a computer to check mathematical proofs.[4] The company said the average result used computing equivalent to roughly three hours of ChatGPT Pro thinking.[4] Its mathematical advisory group recommended releasing results without waiting for full formalization, and OpenAI said roughly half were released unconfirmed.[3] That distinction matters: the repository’s formalized proofs are not evidence that every released result had already been formally checked.

The withdrawals follow a much larger release: OpenAI published 722 preprints on October 6 about purported progress on 372 mathematics problems across several fields.[3] OpenAI says it welcomes scrutiny and feedback, will correct identified errors promptly, and will withdraw papers when it cannot find fixes.[3] A statement reported by Retraction Watch argued that releasing more than 700 files at once demonstrated power rather than scholarship and urged mathematicians to discontinue their work with OpenAI; more than 8,000 researchers endorsed the sentiments.[3] The repository update’s speaker said formalizations and noticed errata would continue to be added.[2]