Physicist corrects record: OpenAI's Lean proof shows Yang–Mills construction is interacting
danintheory · x · 2026-11-14
Physicist Scott Armstrong publicly corrected his earlier assessment of OpenAI's Lean formalization: his prior claim that the construction was not shown to be non-Gaussian was misleading.
Key points:
- The Lean code does prove the theory is not free Yang–Mills: in the free theory the trace of the stress tensor vanishes identically, while in the Lean construction it is nonzero and matches predictions from asymptotic freedom and UV RG computations.
- It proves something stronger: the theory cannot be described by Wick polynomials of any finite set of ordinary free fields.
- Armstrong confirms the theory is interacting; what remains unproved is a stronger, more technical statement about building it out of more free fields.
The correction strengthens the case that OpenAI's Lean project made a substantive contribution to the Yang–Mills mass gap formalization.
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