# [Withdrawal notice: The rational Hodge conjecture for products of K3 surfaces](hodge-conjecture-products-k3.pdf)

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**Withdrawn on October 6, 2026.**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](https://github.com/openai/math/blob/main/preprints/Algebraicity-of-Weil-classes-on-split-abelian-eightfolds-September-18-2026/paper.pdf). 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](https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/The-rational-Hodge-conjecture-for-products-of-K3-surfaces-October-4-2026/hodge-conjecture-products-k3.pdf)  
Repository revision: `adc7f1241b42e322a6451854ab7e4b4c146bf78a`.