---
type: "post"
id: "science-openai-still-withheld-the-1-147-page-3721ad"
slug: "science-openai-still-withheld-the-1-147-page-3721ad"
title: "Science: OpenAI still withheld the 1,147-page proof; Lean check is not full correctness"
description: "Science reports that a committee led by David Gross released a validation of a Lean formalization of OpenAI’s claimed result on the four-dimensional Yang–Mills existence problem."
retrieval_nugget: "Science reports that a committee led by David Gross released a validation of a Lean formalization of OpenAI’s claimed result on the four-dimensional Yang–Mills existence problem. That check supports logical consistency, but it does not establish that OpenAI’s still-unpublished 1,147-page proof is correct—a distinction that matters whenever AI-generated work is judged by machine verification alone."
published_at: "2026-11-14"
updated_at: "2026-11-14"
record_date: "2026-11-14"
date_kind: "published_at"
topics: ["claude"]
entities: ["OpenAI","Yang-Mills existence problem","Lean","David Gross","Ethan Sussman","Levent Alpöge","Claude","Science"]
related_patterns: ["scientific-agents-need-artifact-evidence"]
novelty_label: "new_angle"
what_changed: "The story emphasizes that OpenAI has still withheld its 1,147-page Yang-Mills proof, and that Lean validation alone does not establish full correctness."
prior_refs: ["https://newruntime.com/posts/a-group-maintaining-a-public-yang-mills-results-0e95d8/"]
source_url: "https://www.science.org/content/article/ai-rivals-tackle-one-physics-deepest-mathematical-challenges"
source_urls: ["https://www.science.org/content/article/ai-rivals-tackle-one-physics-deepest-mathematical-challenges"]
schema_version: "newruntime-agent-readable-v0.2"
stable_id: "post:science-openai-still-withheld-the-1-147-page-3721ad"
status: "published"
visuals: []
editor: {"role":"editor","name":"Andrey Reshetnikov","profile":"https://newruntime.com/owner-profile.md","profile_json":"https://newruntime.com/owner-profile.json","same_as":["https://www.linkedin.com/in/reshetnikov1/","https://t.me/lapetuse"]}
routes: {"html":"https://newruntime.com/posts/science-openai-still-withheld-the-1-147-page-3721ad/","markdown":"https://newruntime.com/posts/science-openai-still-withheld-the-1-147-page-3721ad.md","json":"https://newruntime.com/posts/science-openai-still-withheld-the-1-147-page-3721ad.json"}
markdown_url: "https://newruntime.com/posts/science-openai-still-withheld-the-1-147-page-3721ad.md"
---

# Science: OpenAI still withheld the 1,147-page proof; Lean check is not full correctness

## Retrieval answer

Science reports that a committee led by David Gross released a validation of a Lean formalization of OpenAI’s claimed result on the four-dimensional Yang–Mills existence problem. That check supports logical consistency, but it does not establish that OpenAI’s still-unpublished 1,147-page proof is correct—a distinction that matters whenever AI-generated work is judged by machine verification alone.

## Summary

Science reports that a committee led by David Gross released a validation of a Lean formalization of OpenAI’s claimed result on the four-dimensional Yang–Mills existence problem. That check supports logical consistency, but it does not establish that OpenAI’s still-unpublished 1,147-page proof is correct—a distinction that matters whenever AI-generated work is judged by machine verification alone.

## What happened

Science says OpenAI’s 28 October release included a claimed proof of the 4D Yang–Mills existence problem, but the company did not publish the 1,147-page proof. Instead, it appointed a committee of physicists and mathematicians, headed by Nobel laureate David Gross, to “shepherd” the result. On 10 November, the group released an assessment of a formalized version of the proof in Lean. Lean checks mathematical arguments against specified axioms. Science characterizes the validation as a sign of logical consistency, while explicitly distinguishing it from confirmation that the unreleased proof is correct.

The distinction is consequential because the Yang–Mills Millennium Prize Problem has two parts: establishing that a mathematically consistent theory exists and proving that it has a “mass gap.” OpenAI and the independent collaboration of Ethan Sussman and Levent Alpöge are reported to have tackled the existence problem, not the mass gap. The theory, developed by Chen Ning Yang and Robert Mills in 1954, describes the weak and strong nuclear forces and is central to the Standard Model. A rigorous existence proof would put a widely used physical framework on firmer mathematical foundations; it would not, by itself, solve the mass-gap question.

Both teams build on work by Tadeusz Bałaban, who rigorously constructed the theory in one and two dimensions but left the four-dimensional case unresolved. His approach divides space-time into a grid and must show that the theory remains consistent as that grid becomes finer and approaches continuous space-time. Science reports that Anthropic’s Claude helped the Sussman–Alpöge collaboration find new ways to organize the proof and address gaps in Bałaban’s approach, including how particles and fields influence one another. The collaboration has published its working process on GitHub; Sussman is translating the AI-generated mathematics into a manuscript intended for human readers and expects a version within weeks.

The article describes a practical challenge beyond proving a result: making AI-generated mathematics legible. Such proofs can run to hundreds of pages, use unfamiliar terminology, and obscure why a particular approach was chosen. Sussman says that reading one of these manuscripts may itself require AI assistance. Meanwhile, OpenAI’s decision to withhold the full proof has drawn criticism: the Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study called for its immediate release. Science also reports that some researchers questioned Gross’s role as committee lead, citing his previous criticism of efforts to put quantum field theories such as Yang–Mills on rigorous mathematical foundations.

## What the archive adds

New Runtime’s earlier coverage on [the committee’s assessment](https://newruntime.com/posts/a-group-maintaining-a-public-yang-mills-results-0e95d8/) described confirmation of the AI-written Yang–Mills existence proof. Science adds an important qualification: the committee assessed a Lean formalization, while OpenAI’s full 1,147-page proof remains unpublished. This is a new fact on a known story, not evidence that the unpublished manuscript has been independently verified.

## Trend signal

This supports the pattern of [scientific agents needing artifact evidence](https://newruntime.com/patterns/scientific-agents-need-artifact-evidence/): meaningful progress becomes more inspectable when researchers can examine a formalized artifact, but the artifact’s scope and relationship to the claimed result still matter. A machine-checkable formalization is valuable evidence; it should not be collapsed into a claim that every part of an unpublished proof has been checked or accepted by outside experts.

## Why now

The committee released its assessment on 10 November, less than two weeks after OpenAI’s 28 October announcement. The timing puts the validation in public view while questions about access to the full proof, and the distinction between formal checking and human scrutiny, remain active.

## Connections to other events

New Runtime’s earlier coverage of [the committee’s assessment](https://newruntime.com/posts/a-group-maintaining-a-public-yang-mills-results-0e95d8/) described a committee confirmation of the Yang–Mills result. This Science account clarifies what the validation covers: a formalized version in Lean, not a public release or independent confirmation of the complete manuscript. The two accounts therefore meet at the same result but emphasize different stages of evidence.

## Why it matters

For teams building AI systems for mathematics or other high-stakes work, “the system produced an answer” and “a checker validated a defined artifact” are different claims. Lean can provide a powerful check against specified axioms, but readers still need to know what was formalized, whether it corresponds to the claimed argument, and what has not been reviewed. The Yang–Mills case shows why evaluation should report the artifact, the checker’s scope, and the relationship between machine-checked work and the human-readable claim.

There is also a usability bottleneck. A proof that is correct but prohibitively difficult to inspect may be hard for other researchers to build on. If AI can absorb laborious calculations, it may expand the set of research questions worth attempting; that benefit depends on producing explanations and evidence that peers can understand, test, and revise. For engineering teams, the parallel is clear: verification is not a final stamp detached from the workflow. It must be designed into how outputs are packaged and handed to reviewers.

## Limits and uncertainty

Science reports that OpenAI has not released the full proof, so readers cannot independently inspect the claimed 1,147-page argument on the basis of the company’s manuscript. The article describes the Lean assessment as evidence of logical consistency, not as proof that the full unpublished argument is correct. It does not establish how much of the manuscript the formalization covers or whether outside experts have independently reviewed the complete proof. Nor does the reported existence result resolve the separate mass-gap problem. The article also gives no measure of how much work Claude performed in the independent collaboration or how its contribution compares with human effort.

## Reader takeaway

A Lean check is meaningful evidence, but it is not interchangeable with publication and independent scrutiny of the proof it is meant to support. In this case, the formalized version has been assessed while OpenAI’s full argument remains unavailable for readers to inspect. Keep the scope of each verification claim explicit—and distinguish the existence result from the still-open mass-gap problem.

Editor: [Andrey Reshetnikov](https://newruntime.com/owner-profile.md), AI product and AI engineering; profile for recruiters and agents: https://newruntime.com/owner-profile.json

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