# OpenAI withdraws three math manuscripts over a sign error > OpenAI withdrew three math manuscripts over a sign error. The notices identify the failed proof step, preserve earlier PDFs and leave the claims unproved. By BIG CHANGE Editorial Published: 2026-10-08T16:17:52.496Z Updated: 2026-10-08T22:15:14.321Z Canonical: https://bigchange.ai/blog/openai-withdraws-three-math-manuscripts-sign-error ![A plain wall-mounted blackboard bears a single minus sign over a faint, partly erased plus-shaped chalk mark; a small eraser rests on its attached ledge.](https://bigchange.ai/api/media/file/openai-math-sign-correction-hero-v1.png) AI-generated conceptual illustration by BIG CHANGE. The board and marks are symbolic; no real proof, source document, repository, review or theorem validation is depicted. OpenAI has withdrawn three connected manuscripts from its public mathematics collection after finding a sign error in the first paper's proof. The company's [repository history](https://github.com/openai/math/blob/main/history.md), under an October 7 entry, also records revisions to 14 other manuscripts and updated references in 13 more. The three withdrawal notices themselves are dated October 6. They identify a gap in the proofs, not a disproof of the mathematical statements. ## The big change - **What changed:** OpenAI replaced three manuscripts with withdrawal notices. It says one sign error defeated a cancellation step used in the first paper and a construction on which the other two relied. - **Why it matters:** Anyone citing or building on these particular claims now has a precise notice and an archived version to examine. The original proofs cannot be treated as established on the strength of their public release. - **What to watch:** The repository promises to preserve earlier versions and record revisions. Independent review must address each corrected statement and proof; the change log alone cannot establish that the rest of the collection is sound. ## Where the proof stopped The first withdrawn paper, *Algebraicity of Weil classes on split abelian eightfolds*, claimed to establish an algebraicity result in a specific setting of abelian varieties. Its [withdrawal notice](https://github.com/openai/math/blob/main/preprints/Algebraicity-of-Weil-classes-on-split-abelian-eightfolds-September-18-2026/README.md) explains the problem in the paper's own signed double-point convention. The proof began with a count of `-m`, where `m` is positive. It assigned each of `m` reverse stabilization traces a sign of `+1`, making the count appear to cancel to zero. OpenAI now says each trace has sign `-1` because of the opposite source orientations of two branches of the standard cusp. On that account, the count becomes `-2m`, not zero. The cancellation theorem invoked at that step requires a zero signed double-point count. OpenAI says the proof therefore does not support its subsequent oriented-surgery and embedded-brane construction, or establish the paper's claimed theorem. The notice does **not** say that the theorem's statement is false. The other two notices trace their gap to an adaptation of that construction. OpenAI says the claimed algebraicity theorem in [*Algebraicity of Kuga–Satake Correspondences for K3 Surfaces*](https://github.com/openai/math/blob/main/preprints/Algebraicity-of-Kuga-Satake-Correspondences-for-K3-Surfaces-October-3-2026/README.md) remains unproved. Its notice for [*The rational Hodge conjecture for products of K3 surfaces*](https://github.com/openai/math/blob/main/preprints/The-rational-Hodge-conjecture-for-products-of-K3-surfaces-October-4-2026/README.md) says the same about that paper's claimed theorem for products of projective K3 surfaces. These are the three manuscripts the history file names; the notices do not identify unrelated results in the collection as withdrawn. Each notice links a pre-withdrawal PDF at repository revision `adc7f1241b42e322a6451854ab7e4b4c146bf78a`. BIG CHANGE checked those three notice links and their archived PDF destinations. This was an inspection of public documents, not a mathematical refereeing of the arguments or a Lean proof check. ## A broader revision, with narrower conclusions In the same [October 7 history entry](https://github.com/openai/math/blob/main/history.md), OpenAI says it revised 14 other manuscripts. It describes proof repairs and changes to statements, hypotheses and dependencies across several subjects, plus one obsolete-citation correction. Thirteen additional manuscripts received updated references to revised companion editions, according to the entry. OpenAI also reports six more formalizations, bringing its count of formalized top-line results to 300 of 719, or about 42%. Those figures describe OpenAI's account of its repository update. They do not measure the soundness of the revised arguments or show that every claim in a formalized manuscript has been checked. The repository [README](https://github.com/openai/math) itself says the collection contains work at different stages of verification and warns that some unformalized results may have issues. We did not find a timely independent mathematical assessment of this specific sign error and its dependent proofs during this reporting. The October 6 release placed a large collection of AI-produced manuscripts into public view. Our earlier [repository inspection](https://bigchange.ai/blog/openai-math-repository-manuscripts-formal-proofs) explains how to pin a version and distinguish a manuscript from its formal proof artifacts; our [opinion on research-review capacity](https://bigchange.ai/blog/ai-research-discovery-review-capacity) discusses the work needed to assess a release of this size. The new withdrawal record gives a concrete reason to preserve that distinction. For these three papers, OpenAI has identified which proof step failed and kept the previous PDFs accessible. Whether a future proof establishes any of their statements remains an open mathematical question. ## Sources & further reading OpenAI's [repository history](https://github.com/openai/math/blob/main/history.md) records the three withdrawals, 14 manuscript revisions, 13 companion-reference updates and formalization count under October 7, 2026. The individual [Weil-class](https://github.com/openai/math/blob/main/preprints/Algebraicity-of-Weil-classes-on-split-abelian-eightfolds-September-18-2026/README.md), [Kuga–Satake](https://github.com/openai/math/blob/main/preprints/Algebraicity-of-Kuga-Satake-Correspondences-for-K3-Surfaces-October-3-2026/README.md) and [K3-product Hodge](https://github.com/openai/math/blob/main/preprints/The-rational-Hodge-conjecture-for-products-of-K3-surfaces-October-4-2026/README.md) notices explain the claimed gaps, label the withdrawals October 6 and link archived PDFs at a fixed revision. These are OpenAI's records; they are direct evidence of what the company disclosed, not independent proof review. OpenAI's [October 6 announcement](https://openai.com/index/sharing-ai-progress-in-mathematics/) explains the initial public release and planned additions. BIG CHANGE examined the current history file, the three notices and their archive links on October 8. We did not execute Lean, inspect every revised manuscript or verify the mathematics independently. ## Sources - [OpenAI math repository history](https://github.com/openai/math/blob/main/history.md) — OpenAI's description of the sign error, three withdrawals, fourteen revisions, companion-reference updates and additional formalizations. - [OpenAI math repository](https://github.com/openai/math) — Inspect the affected manuscript notices, archived versions and revision metadata; these establish the artifact status, not independent correctness. - [Sharing AI progress in mathematics](https://openai.com/index/sharing-ai-progress-in-mathematics/) — Context only for the initial collection; do not repeat its broad claims as validation.