OpenAI Withdraws Three Math Papers Due to Sign Error, Updates 14 Manuscripts

OpenAI has withdrawn three mathematical manuscripts from its openai/math repository following the discovery of a critical error. The issue originated in "Algebraicity of Weil classes on split abelian eightfolds", where a sign error invalidated a stabilization-trace cancellation argument and the construction used by two dependent papers.

Withdrawn Manuscripts

The following three papers have been withdrawn and now carry notices explaining the gap:

• Algebraicity of Weil classes on split abelian eightfolds
• Algebraicity of Kuga–Satake Correspondences for K3 Surfaces
• The rational Hodge conjecture for products of K3 surfaces

Fixes and Updates

In addition to the withdrawals, OpenAI revised 14 other manuscripts to address proof repairs, corrected statements, and clearer hypotheses. Key updates include:

• Lipschitz heights and Ashkin–Teller currents (4 manuscripts): Repaired crossing, boundary-attachment, conditioning, and convergence arguments.
• Kähler minimal model programs and abundance (6 manuscripts): Expanded positivity and contraction arguments.
• Taming and hypersymplectic deformation (2 manuscripts): Corrected cone-equality claims and removed unnecessary dependencies.
• Incompressible Box Transport and Finite Computation: Revised torus-projection and common-clock estimates.
• Exact Birch–Swinnerton-Dyer Formula: Removed an obsolete citation.

Consequently, 13 additional manuscripts were updated to cite the revised editions of companion papers.

Formalization Progress

OpenAI added 6 formalizations and 5 other additions covering supporting results. This brings the total percentage of top-line results formalized to 300 / 719 = ~42%.