{"id":"openai-math/Algebraicity-of-Kuga-Satake-Correspondences-for-K3-Surfaces","pdf":"https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Algebraicity-of-Kuga-Satake-Correspondences-for-K3-Surfaces-October-3-2026/manuscript.pdf","url":"https://github.com/openai/math/tree/main/preprints/Algebraicity-of-Kuga-Satake-Correspondences-for-K3-Surfaces-October-3-2026","tags":["k3-surfaces","kuga-satake","algebraic-cycles","withdrawn"],"score":0,"title":"Algebraicity of Kuga–Satake Correspondences for K3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 algebraicity theorem unproved. This withdrawal concerns the proof; it does not assert that the mathematical statement is false.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":2,"published":"2026-10-03","reactions":{},"withdrawn":true,"discussion":[{"url":"https://x.com/Frances01896069/status/2108167317385249123","date":"2026-10-08","kind":"x","added":"2026-10-24","author":"Francesco Maggi","handle":"Frances01896069"},{"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[OAI26a, OAI26b, OAI26c] claimed to prove cases of the Hodge conjecture via homological mirror symmetry, before being withdrawn by OpenAI.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"}