OpenAI has withdrawn three mathematics research papers after discovering a sign error that invalidated a key argument. The affected manuscripts 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,” according to OpenAI’s official GitHub repository.
The sign error compromised a stabilization-trace cancellation argument and the construction used by the three dependent papers. OpenAI has updated the papers’ README files to explain the gap and provide links to the archived versions of the withdrawn manuscripts. This action follows a broader review process where 14 other manuscripts were revised with proof repairs, corrected statements, and clarified hypotheses.
The withdrawal highlights the challenges of maintaining mathematical rigor in advanced AI research documentation. OpenAI’s transparency in documenting the error and linking to the archived manuscripts sets a precedent for accountability in AI-related academic work. The revisions to other manuscripts include improvements in arguments related to Lipschitz heights, Kähler minimal model programs, and hypersymplectic deformation, reflecting ongoing efforts to strengthen their research outputs.
The withdrawn papers remain accessible through the version notes on OpenAI’s GitHub, ensuring continued availability for reference despite the retraction. The repository’s history file details these changes, providing a clear record of the updates and withdrawals.