OpenAI · w-003 · 2026-10-04 · Withdrawn preprints
The rational Hodge conjecture for products of K3 surfaces
preprints/The-rational-Hodge-conjecture-for-products-of-K3-surfaces-October-4-2026
Withdrawn. This is not a current result. The authors are OpenAI.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. Withdrawn. This is not a current result. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
# Withdrawal notice: The rational Hodge conjecture for products of K3 surfaces OpenAI **Withdrawn on October 6, 2026.** The proof relies on an adaptation of the flawed stabilization-trace construction in Algebraicity of Weil classes on split abelian eightfolds. The sign error in that construction prevents the required signed-double-point cancellation. The resulting gap leaves this paper's claimed rational Hodge theorem for products of projective K3 surfaces unproved. This withdrawal concerns the proof; it does not assert that the mathematical statement is false. ## Archived manuscript Pre-withdrawal PDF Repository revision: adc7f1241b42e322a6451854ab7e4b4c146bf78a.
Preprint source and Lean scope
The abstract above is the catalogue abstract. The sections below are the full preprint source, 0 sections. This page is not only the abstract. The manuscript file is loading.
No Lean scope note is in the repository for this family. The preprint source below is still the full manuscript, not only the abstract. No compilation is asserted.