{"id":"openai-math/Algebraicity-of-Weil-classes-on-split-abelian-eightfolds","pdf":"https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Algebraicity-of-Weil-classes-on-split-abelian-eightfolds-September-18-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Algebraicity-of-Weil-classes-on-split-abelian-eightfolds-September-18-2026","tags":["algebraic-geometry","hodge-conjecture","weil-classes"],"score":-1,"title":"Algebraicity of Weil classes on split abelian eightfolds","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"Withdrawal notice: The proof contains a sign error in the stabilization-trace argument used to obtain negative double points. In the manuscript's signed double-point convention, write $I(f_1)=-m$ with $m>0$. The proof assigns each reverse stabilization trace sign $+1$ and therefore claims that inserting $m$ such traces makes the signed count zero. Accounting for the opposite source orientations of the two branches of the standard cusp gives sign $-1$ for each reverse trace in this convention. The resulting count is therefore $$I_{\\mathrm{new}}=I(f_1)-m=-2m\\ne0.$$ The Eliashberg-Murphy…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":2,"published":"2026-09-18","reactions":{"down":1,"👎":1},"withdrawn":true,"discussion":[{"url":"https://x.com/Frances01896069/status/2108167317385249123","date":"2026-10-08","kind":"x","added":"2026-10-24","author":"Francesco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[OAI26a, OAI26b, OAI26c] claimed to prove cases of the Hodge conjecture via homological mirror symmetry, before being withdrawn by OpenAI.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"}