OpenAI Withdraws 3 Math Papers

A sign error undermined a stabilization-trace cancellation argument and the construction relied on by two related works, prompting withdrawal of three manuscripts: "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." Each withdrawn paper now carries a notice explaining the gap and linking to the archived manuscript. The record also documents broader corrective work across the collection rather than isolated retractions.

Fourteen other manuscripts were revised with repaired proofs, tightened statements, clearer hypotheses and dependency notes, and one obsolete citation removed. Notable clusters of fixes include four papers on Lipschitz heights and Ashkin-Teller currents (crossing, boundary-attachment, conditioning and convergence arguments plus extra real‑Lipschitz interface work); six on Kähler minimal model programs and abundance (expanded positivity and contraction arguments and clarified input hypotheses); two on taming and hypersymplectic deformation (corrected a cone-equality claim, added a strict‑inclusion example, removed an unnecessary cone‑comparison dependency); a revision to torus‑projection and common‑clock estimates in Incompressible Box Transport and Finite Computation; and a cleanup in an exact Birch-Swinnerton‑Dyer paper. Thirteen additional manuscripts updated citations to the revised editions. Six new formalizations and five supporting additions raise the proportion of top‑line results formalized to 300/719 ≈ 42%.