OpenAI said it is withdrawing three pre‑print math papers after a sign error was found in a core proof. The error makes a stabilization‑trace cancellation step invalid, which also undermines two later papers that built on the result. The withdrawn manuscripts are: • Algebraicity of Weil classes on split abelian eightfolds • Algebraicity of Kuga–Satake Correspondences for K3 Surfaces • The rational Hodge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 OpenAI added notices to the papers and linked to the archived versions so readers can see the gap.
What else was updated?
Alongside the withdrawals, OpenAI fixed 14 other manuscripts. The fixes address proof gaps, clarify hypotheses, and correct citations. Areas touched include Lipschitz heights, Kähler minimal model programs, and hypersymplectic deformation. Thirteen additional papers were updated to cite the revised versions of related work. The organization also added six new formalizations, bringing the proportion of top‑line results formally verified to about 42 % (300 of 719).
Why it matters
For mathematicians who follow OpenAI’s formal‑verification work, the retraction means a gap in the literature that may affect any research that cited those three results. Readers can now see exactly where the error occurred and avoid building on the faulty proof. The broader community still benefits from the 14 repaired papers and new formalizations, which improve the reliability of OpenAI’s math library.
