One sign error pulls three OpenAI math papers

One minus sign in the wrong place took down three papers at once. According to the October 7, 2026 entry in the history file of OpenAI's math repository on GitHub, a sign error in "Algebraicity of Weil classes on split abelian eightfolds" invalidates a stabilization-trace cancellation argument, along with a construction that two other papers built on.

At a glance

• OpenAI withdrew three manuscripts on Weil classes, Kuga–Satake correspondences and the rational Hodge conjecture for K3 products, and each now carries a notice explaining the gap and linking to the archived version.
• The same update revised 14 other manuscripts, refreshed citations in 13 more, and added 6 Lean formalizations, bringing machine-checked top-line results to 300 of 719, or about 42%.
• The history entry does not say who caught the sign error or how, and 419 of 719 top-line results still have no Lean formalization behind them.

If you missed it, OpenAI's README on GitHub says the company widened its evaluations to open research problems after its existing math evaluations saturated, and that some outputs build on earlier model results. Per the same README, the vast majority of results came from one procedure run on an unreleased internal model. That model was posed approximately 4,000 problems and used on average three hours of ChatGPT Pro thinking compute per result.

One sign error in an eightfold paper took two K3 papers with it

The broken paper is "Algebraicity of Weil classes on split abelian eightfolds". With the sign wrong, its stabilization-trace cancellation argument no longer goes through. The construction it supported was also used by "Algebraicity of Kuga–Satake Correspondences for K3 Surfaces" and "The rational Hodge conjecture for products of K3 surfaces", so OpenAI withdrew all three.

None of them was deleted. The README of each withdrawn paper now explains the gap and links to the archived manuscript, and updated papers keep their earlier editions reachable through version notes. According to the README on GitHub, OpenAI has committed to recording corrections as new versions while previously released versions stay accessible.

Why would one error sink three papers? The GitHub README explains that a family groups related papers: a principal result, companion arguments, consequences or alternative proofs. Think of floors resting on one slab: crack the slab, and the floors above are condemned even if their own carpentry is sound.

Fourteen manuscripts got proof repairs and 13 more got new citations

The withdrawals were the sharpest part of a larger cleanup. The same entry lists 14 other manuscripts revised with proof repairs, corrected statements, clearer hypotheses and dependencies, and one correction to an obsolete citation:

• Lipschitz heights and Ashkin–Teller currents, 4 manuscripts: repaired crossing, boundary-attachment, conditioning and convergence arguments, plus more work on the real-Lipschitz interface proof.
• Kähler minimal model programs and abundance, 6 manuscripts: expanded positivity and contraction arguments, with clearer notes on which inputs are used and their hypotheses.
• Taming and hypersymplectic deformation, 2 manuscripts: a corrected cone-equality claim in "Taming implies compatibility", a new strict-inclusion example, and an unnecessary cone-comparison dependency removed.
• "Incompressible Box Transport and Finite Computation": revised torus-projection and common-clock estimates.
• "Exact Birch–Swinnerton-Dyer Formula from Low Selmer Corank": an obsolete introductory citation to a removed supporting manuscript taken out.

The fixes rippled outward: 13 additional manuscripts were updated to cite the revised editions of companion papers, which changed references and version dates. OpenAI's own summary posted to Hacker News counts the batch as 6 new Lean formalizations, 19 modifications and 3 withdrawals.

300 of 719 top-line results now have a Lean formalization

The update added 6 formalizations and 5 other additions covering supporting results, taking formalized top-line results to 300 of 719, about 42%. Lean, as TNW explains, is a programming language in which a proof is written so a computer can check it, and the repository points to Comparator instructions for additional checking.

The collection holds results at different stages of verification, and not all of them have Lean formalizations. The README on GitHub says so directly and promises to fix problems quickly:

Some of the unformalized results could have issues

The repo opened on October 6 with 722 manuscripts in 372 families

The repository launched on Tuesday, October 6, 2026 with 722 manuscripts in 372 families. The README now lists 719 manuscripts in the same 372 families, which matches the three withdrawals. According to AICoder, none of the results had been peer reviewed at launch, and the model has not been released.

According to TNW, NYU mathematician Tristan Buckmaster said at launch, "I don't think they've done their sort of due diligence at all", while MIT's Andrew Sutherland advised treating single-agent claims as unverified until others can run the model and repeat the results. TNW also reports that the same model produced OpenAI's Navier-Stokes proof the previous month.

The IAS-hosted Advisory Group on Mathematics and AI (AGMAI), per TNW, asked labs in its 29 September guidelines to publish the prompts, time and compute cost behind each result. After the release, TNW reports, the group said its advice was not an endorsement.

The history entry says what broke but not who noticed it, how, or whether the broken step in the eightfold paper had any Lean formalization behind it. In our view, leaving the withdrawn manuscripts online behind a notice is the right design choice, since anyone who relied on the K3 results can see exactly where the argument failed.

Whether the K3 results come back

OpenAI says it will keep updating the repository with new formalizations and any errata it notices, and the history file is where those entries appear. No schedule has been given. The entry also does not say whether the three withdrawn results will be repaired and restored or stay withdrawn. Another figure to watch is the 419 top-line results that still have no Lean formalization.