# OpenAI Yang-Mills Lean Proof: Gross Group Validation and Public Release

> Source: <https://explainx.ai/blog/openai-yang-mills-gross-group-lean-validation-november-2026?utm_source=rss&utm_medium=feed&utm_campaign=blog>
> Published: 2026-11-11 00:00:00+00:00

On **November 9, 2026**, the **Yang-Mills Working Group** chaired by **[David Gross](https://www.kitp.ucsb.edu/statement-by-the-yangmills-working-group?ref=explainx)** announced it would publish **OpenAI''s Lean formalization** of **pure Yang-Mills existence** the next day. By **November 11**, the **`OpenAI-YM-20261028`** repository on GitHub is **public**, and the group''s **[assessment PDF](https://github.com/yang-mills-group/YM/blob/main/docs/assessment-1.pdf?ref=explainx)** is linked from its **[third committee statement](https://www.kitp.ucsb.edu/sites/default/files/3rd-Statement-About-Quantum-YangMills-Theory_Nov-9.pdf?ref=explainx)**.

This is the first **machine-checkable release** from the physics shepherding process [OpenAI described on October 26](https://openai.com/index/building-scientific-understanding-with-academic-communities?ref=explainx). It does **not** close the **Clay mass gap** question that [RoundSquare](https://explainx.ai/blog/round-square-lean-yang-mills-mass-gap-peano-openai-what-is-claimed-2026) and social posts keep arguing about.

## TL;DR

| Question | Answer | 
|---|---|
| What shipped? | Lean code + expert **assessment** on**existence** | 
| Who signed the release? | Douglas, **Gross** , Jaffe, Klebanov, Nekrasov | 
| Mass gap / confinement? | Still **open** , per committee''s prior statements | 
| OpenAI repo | [github.com/yang-mills-group/OpenAI-YM-20261028](https://github.com/yang-mills-group/OpenAI-YM-20261028?ref=explainx) | 
| Read this with | [October triple-result hub](https://explainx.ai/blog/openai-exponential-time-hypothesis-false-kakeya-yang-mills-three-results-lean-collaborations-2026) | 

## What the committee actually claims

The **[November 9 PDF](https://www.kitp.ucsb.edu/sites/default/files/3rd-Statement-About-Quantum-YangMills-Theory_Nov-9.pdf?ref=explainx)** names two artifacts:

1. **Full Lean code** OpenAI submitted**October 28, 2026** — now at**[OpenAI-YM-20261028](https://github.com/yang-mills-group/OpenAI-YM-20261028?ref=explainx)** .
2. A **validation document** summarizing checks on the October 28 submission. The group's**[YM repository README](https://github.com/yang-mills-group/YM/blob/main/README.md?ref=explainx)** states that, in its opinion, the formalization constructs a**Wightman QFT** as a scaling limit of**Wilson lattice gauge theory** — existence machinery,**not** a mass-gap proof.

The wording is careful. It validates **existence** under the definitions the committee accepts. It does **not** claim a public proof of **Δ greater than zero** on **R⁴** in the Clay Millennium sense.

The group''s **[first statement](https://www.kitp.ucsb.edu/sites/default/files/1st-Statement-About-Quantum-YangMills-Theory_Oct-26.pdf?ref=explainx)** already said **confinement and the mass gap remain very important open challenges**. The **[second statement](https://www.kitp.ucsb.edu/sites/default/files/2nd-Statement-About-Quantum-YangMills-Theory_Nov-3.pdf?ref=explainx)** described **definition alignment** work before release.

Green verification seal evoking machine-checked Lean review of OpenAI Yang-Mills formalization

## Timeline: from model output to GitHub

OpenAI''s **[October 26 post](https://openai.com/index/building-scientific-understanding-with-academic-communities?ref=explainx)** gave these dates for Yang-Mills:

- **September 9, 2026** — natural-language existence proof produced inside OpenAI.
- **October 16, 2026** — Lean formalization finished.
- **October 28, 2026** — Lean package delivered to the Gross group (per the November 9 statement).

Between **November 3** and **November 9**, the committee said it was checking that **definitions match standard statements** and that the **formalization aligns with informal treatment**. The **November 10** release date was announced **one day ahead**, matching the procedure in the second statement.

For ETH and Kakeya, OpenAI shipped public Lean earlier. Yang-Mills stayed **withheld** until this shepherding finished — the pattern we tracked in **[our launch explainer](https://explainx.ai/blog/openai-exponential-time-hypothesis-false-kakeya-yang-mills-three-results-lean-collaborations-2026)**.

## What is in the GitHub repository

The published repo description reads **"OpenAI construction of pure Yang-Mills obtained 10/28/2026"**. It is **Lean 4** source intended for **community inspection**, not a polished paper.

If you maintain **scientific agent** pipelines, treat it like any large third-party formal artifact:

- Pin a **Lean toolchain** version before you Mathlib-pin.
- Read **`#print axioms`** on modules you depend on.
- Compare **theorem statements** against the informal problem sheet in the assessment PDF.

The committee credits **Ron Nissim** and **Fred Rajasekaran** on the assessment work. That mirrors how human peer review often splits **authorship** (OpenAI) from **verification reporting** (the group).

Chalkboard-style diagram for Yang-Mills existence proof and Clay mass-gap debate context

## Mass gap, RoundSquare, and headline confusion

Two parallel stories collide in headlines:

| Thread | Claim type | Public artifact | 
|---|---|---|
| **Gross group release** | **Existence** of pure Yang-Mills in accepted formalization | Lean repo + assessment | 
| **[RoundSquare](https://explainx.ai/blog/round-square-lean-yang-mills-mass-gap-peano-openai-what-is-claimed-2026)** | **Impossibility** of OS axioms + strict gap on**R⁴** | Public Lean + Zenodo preprint | 
| **Clay prize (popular)** | Existence **and** mass gap**Δ greater than 0** | Still contested in public formalizations | 

Social posts that say **"Peano disproved the $100B proof"** usually mean RoundSquare''s **infrared argument**, not a refutation of every line in OpenAI''s withheld package. Now that **existence Lean** is public, readers can ask sharper questions: **do the definitions in `OpenAI-YM-20261028` match the assessment''s reading, and do they match the Clay statement Jaffe and Witten published?**

We are not physicists signing off on QFT measure theory. The **actionable read** for builders is **definition alignment**: automated provers are only as meaningful as the **formal statement** they close.

## How this compares to other lab Lean collaborations

Anthropic and other labs have shipped **formal math** with outside audits — see **[Aaronson–Ambainis conjecture coverage](https://explainx.ai/blog/physical-superintelligence-aaronson-ambainis-conjecture-proof-anthropic-model-lean-claimed-vs-verified-2026)** and **[Opus formalizing CPython](https://explainx.ai/blog/opus-5-5-cpython-lean-formalization-418-bugs-2026)**. The Yang-Mills arc adds **months of withholding** and a **Nobel-laureate committee** as gatekeeper.

That matters for **agent evals** and **research harnesses**:

- **Time-to-public** can exceed**time-to-generate** by an order of magnitude.
- **Custody** may sit with**domain committees** , not the lab blog.
- **Partial releases** (existence first, mass gap later, natural-language write-up later still) are plausible even when Lean exists internally.

## What the assessment says versus what Lean checks

Lean does not read like a physics paper. It is a **dependency graph of definitions**, each theorem pinned to axioms Mathlib already exports or to definitions the submission introduces. The committee''s **[assessment PDF](https://github.com/yang-mills-group/YM/blob/main/docs/assessment-1.pdf?ref=explainx)** is the human-readable map between **informal Yang-Mills existence language** and those formal statements.

When you audit, copy this checklist:

1. **Locate the main existence theorem** in the repo README or top-level module index.
2. Run **`lake build`** with the toolchain file the repo pins; do not mix Mathlib versions blindly.
3. For any claim you care about, run **`#print axioms`** on that theorem — unexpected axioms are a red flag.
4. Compare the formal **gauge group** ,**measure** , and**Hilbert space** wording against Jaffe–Witten and against the committee PDF, not against Twitter summaries.
5. File GitHub issues on **definition mismatches** if you find them; that is how public formal math improves.

The committee thanked **Ron Nissim** and **Fred Rajasekaran** on the assessment — typical for a large formalization where **statement alignment** is as much work as **proof length**.

## AGMAI, withholding, and why release took weeks

The **[Advisory Group on Mathematics and Artificial Intelligence](https://agmai.org/?ref=explainx)** asked OpenAI in late October to release Yang-Mills outputs **without delay** once Lean existed. The **Gross group** chose a slower path: **validate definitions**, then publish **Lean first** while the **1,147-page natural-language package** waits for another quality gate.

That split matters for **research agents**:

| Artifact | ETH / Kakeya (October) | Yang-Mills (November) | 
|---|---|---|
| Lean on GitHub | OpenAI org repos | **yang-mills-group** org | 
| Natural language | Public with Lean | **Still withheld** per committee | 
| Expert gate | Impagliazzo-style CS group | **Physics Nobel-laureate committee** | 
| Prize wording | Complexity / harmonic analysis | **Existence only** in public text | 

If your pipeline ingests **arxiv + GitHub only**, you may now index **existence Lean** but still miss the **full narrative proof** — plan crawlers accordingly.

## Reading list for builders who are not QFT experts

You do not need to master constructive QFT to extract value:

- **Wilson lattice** intuition — why discretization appears before continuum limits.
- **Balaban RG program** — the historical line OpenAI says its proof extends.
- **OS/Wightman axioms** — the package RoundSquare argues is over-constrained on**R⁴** .
- **Clay problem sheet** — the exact conjunction journalists conflate with**existence alone** .

Our **[Millennium prize AI scorecard](https://explainx.ai/blog/millennium-prize-problems-ai-solved-fact-check-2026)** and **[OpenAI 722-manuscript repo guide](https://explainx.ai/blog/openai-722-math-manuscripts-github-repo-what-to-check-2026)** help separate **headline counts** from **checkable artifacts**.

## What people building with formal methods should do next

**Clone and compile.** Start from the committee''s repo URL, not a fork you cannot trace.

**Read the assessment before the lore.** The PDF is the committee''s **summary of checks**, analogous to a referee report''s "main theorem verified" paragraph.

**Separate existence from prize language.** If your product marketing says **"solved Yang-Mills,"** you are ahead of the committee''s own **mass-gap** disclaimer.

**Watch for the natural-language 1,147-page package.** The first statement said the group may release **full LLM proofs** once satisfied with quality. That is a **second drop**; today''s release is **Lean-first**.

**Pair with complexity-news hygiene.** The same October batch included **[ETH and Kakeya Lean](https://explainx.ai/blog/openai-exponential-time-hypothesis-false-kakeya-yang-mills-three-results-lean-collaborations-2026)** with different public timelines. Do not assume one release policy fits all three.

## Implications for AI evals and science agents

Teams building ** theorem-proving agents** should log three metrics on this release:

**Time from generation to public Lean** — roughly **seven weeks** from OpenAI''s stated Lean completion to GitHub, dominated by **human committee** time, not compute.

**Custody model** — artifacts live under a **third-party org**, not the lab that generated them. Your agent must follow redirects and mirror policies.

**Partial claim scope** — automated headline tests should flag posts that say **"Clay solved"** when sources say **existence only**.

Pair with **[AI peer review planted-errors benchmarks](https://explainx.ai/blog/ai-peer-review-planted-errors-benchmark-dawes-institute-2026)** if you score models on **reading referee-style PDFs**, not just compiling Lean.

## Questions readers search after this headline

**Did OpenAI disprove RoundSquare?** Not automatically. RoundSquare targets a **different conjunction** on **R⁴**. Both can be **formally valid** under different statements.

**Can I cite this in production?** Cite the **committee assessment** and **theorem statements you verified**, not uncopied social threads.

**Will API prices change?** No signal in KITP or GitHub releases. This is **science process**, not product pricing.

**Does this help coding agents?** Indirectly — it is another datapoint that **long-horizon formal tasks** can produce **gigabyte-scale artifacts** needing **expert gates** before trust.

## What is still unverified or open

- **Independent mathematicians** beyond the committee may publish critiques of definitions or analytic steps inside the Lean.
- **Clay Mathematics Institute** has not, in sources we checked, issued a prize decision based on this release.
- **Mass gap and confinement** remain**open** in the committee''s own framing.
- **RoundSquare** and**OpenAI existence** may both be**formally consistent** if they formalize**different problem statements** — that is a job for experts, not a headline.

## Related reading

*Repository URLs, committee statements, and OpenAI announcement text are accurate as of November 11, 2026.*