Yang-Mills Working Group validates OpenAI's Lean construction, but mass gap remains unproven
calabi_and_yau · x · 2026-11-11
The Yang-Mills Working Group has released an independent validation of OpenAI's Lean formalization (submitted Oct 28, repo OpenAI-YM-20261028).
Key findings
- The submission proves a relativistic QFT satisfying the Wightman axioms, constructed as a scaling limit of 4D Wilson lattice gauge theory for any simple compact gauge group.
- It does not prove uniqueness of the infinite-volume limit or a mass gap, so it does not settle the Jaffe-Witten formulation of the Millennium Prize Problem.
Validation process
- Clean rebuild, axiom audit, and Comparator check all passed; additional independently formulated Lean checks confirm the construction meets the stated requirements, plus human review of definitions.
- The proof builds continuum correlation functions as a scaling limit at fixed volume, uses compactness for subsequential limits, decomposes into OS-axiom-satisfying pure phases, and applies the Osterwalder-Schrader reconstruction theorem.
- The group states its only tie to OpenAI is using the Astra model for analysis, and has no connection to the Clay Mathematics Institute.
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