---
id: "lib-2026-10-07-history-withdrawal-of-three-mathematical-results"
type: "library"
title: "History: withdrawal of three mathematical results"
lang: "EN"
org: "OpenAI (openai/math repo)"
source_type: "Code"
date: "2026-10-07"
week: "2026-W41"
url: "https://nosov.ai/library/lib-2026-10-07-history-withdrawal-of-three-mathematical-results/"
original_url: "https://github.com/openai/math/blob/main/history.md"
tier: "C"
tier_name: "Weak signal"
tier_reason: "A short changelog entry in OpenAI's own repository; a primary record with counts, but an announcement with no method or external verification attached."
summary_basis: "full-text"
original_minutes: "3"
tags: ["ai technology", "ai for science verification", "research integrity"]
frames: ["verification-capacity"]
---

# History: withdrawal of three mathematical results

Tier C (Weak signal): A short changelog entry in OpenAI's own repository; a primary record with counts, but an announcement with no method or external verification attached.

Summary based on the full text.

## In short

The 7 October 2026 entry in the history log of OpenAI's public `openai/math` repository. The repository README describes its 719 manuscripts as produced by an unreleased internal OpenAI model. A sign error in one paper on Weil classes invalidated its key argument and the construction two other papers relied on, so all three were withdrawn. Fourteen more were repaired, and the share of top-line results with formal Lean proofs reached about 42%.

## Key numbers

- 3: manuscripts withdrawn after a sign error in one proof
- 14: other manuscripts revised with proof repairs and corrected statements
- 300 / 719: top-line results formalized in Lean, about 42%

## What it reports

- Withdrawn: "Algebraicity of Weil classes on split abelian eightfolds" and two dependent papers, on Kuga-Satake correspondences for K3 surfaces and the rational Hodge conjecture for products of K3 surfaces. The cause: a sign error that invalidates a stabilization-trace cancellation argument.
- Withdrawn papers keep notices explaining the gap and link to archived versions.
- 14 manuscripts revised: 4 on Lipschitz heights and Ashkin-Teller currents, 6 on Kähler minimal model programs and abundance, 2 on taming and hypersymplectic deformation, 1 on incompressible box transport, 1 on the Birch-Swinnerton-Dyer formula (an obsolete citation removed).
- 13 additional manuscripts updated only to cite revised companion papers.
- 6 new formalizations and 5 supporting additions, bringing formalized top-line results to 300 of 719 (~42%).
- Per the README: about 4,000 problems were posed, each result averaged three hours of ChatGPT Pro thinking compute, the 719 manuscripts form 372 families, and unformalized results "could have issues".

## How they got it

This is a release note, not a study. Errors were found after publication and corrected as new versions, with older versions kept accessible. Formal verification uses a Lean library and a formalization catalogue in the same repository.

## Limits

- The log does not say who found the error (the model, OpenAI staff or outside mathematicians) or how long it went unnoticed.
- No error rate is given for the 58% of results that are not formally verified.

## Why it matters for companies

Model-generated work at volume needs the same correction machinery as human work: versioning, withdrawal notices and dependency tracking. One sign error took down three papers because two were built on the first, which is how errors spread through any chain of AI-generated analyses. The part that was formally checked is the part you can trust; the remaining 58% carries an explicit warning. Companies producing AI-written reports should know which share of their output has been independently checked and say so.

Original: https://github.com/openai/math/blob/main/history.md