OpenAI's Navier–Stokes solution doesn't match its Lean verification, researcher warns

ValerioCapraro · x · 2026-10-08

Researcher Valerio Capraro flags that OpenAI's claimed Navier–Stokes solution does not match its Lean verification, pointing to a paper's deep warning:

• A Lean-verified proof does not automatically validate the natural-language proof, nor does the formal statement necessarily capture the intended theorem — AI can change an assumption, weaken a statement, or replace the argument during translation.
• The paper identifies at least two mismatches in OpenAI's solution: an estimate claiming four additional input derivatives suffice while the Lean version requires five (a weaker result), and a pressure-flux estimate proved via a different bound and argument.
• It's unclear if these invalidate the whole proof, but the author criticizes OpenAI for flooding the public with claimed breakthroughs nobody can verify — 'epistemia at scale.'

Related event: Cambridge paper argues Lean verification does not certify proofs, targeting OpenAI's Navier-Stokes claim(14 posts)→

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