{"id":"openai-math/The-rational-Hodge-conjecture-for-products-of-K3-surfaces","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","url":"https://github.com/openai/math/tree/main/preprints/The-rational-Hodge-conjecture-for-products-of-K3-surfaces-October-4-2026","tags":["hodge-conjecture","k3-surfaces","algebraic-geometry"],"score":0,"title":"The rational Hodge conjecture for products of K3 surfaces","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"Withdrawal notice: 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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":5,"published":"2026-10-04","reactions":{},"withdrawn":true,"discussion":[{"url":"https://scottaaronson.blog/?p=10169#:~:text=Underscores%20just%20how%20important%20it%20is%20for%20human%20mathematicians","date":"2026-10-07","kind":"web","site":"Shtetl-Optimized","text":"Underscores just how important it is for human mathematicians to go through and understand these things. If I had to place a bet, most of these will stand but this isn’t the last one that will have some bug and need to be retracted … just like with human papers! Pierre Says: Comment #133 October…","added":"2026-10-24","title":"The Mathocalypse"},{"url":"https://x.com/Frances01896069/status/2108167317385249123","date":"2026-10-08","kind":"x","added":"2026-10-24","author":"Francesco Maggi","handle":"Frances01896069"},{"url":"https://x.com/ivanswzhang/status/2110636315746410883","date":"2026-10-15","kind":"x","added":"2026-10-24","author":"Shaowu Zhang","handle":"ivanswzhang"},{"url":"https://x.com/ivanswzhang/status/2111025825588052368","date":"2026-10-16","kind":"x","added":"2026-10-24","author":"Shaowu Zhang","handle":"ivanswzhang"},{"url":"https://arxiv.org/abs/2610.30976","date":"2026-10-22","kind":"web","site":"arXiv.org","text":"The documents [OAI26a, OAI26b, OAI26c] claimed to prove cases of the Hodge conjecture via homological mirror symmetry, before being withdrawn by OpenAI. We discuss the source of the error (but do not analyse the rest of the argument).","added":"2026-10-24","title":"Rigidity, flexibility, and a sign error","author":"Yanki Lekili, Nick Sheridan","record":"arxiv/2610.30976"}],"withdrawn_on":"2026-10-06"}