The trick: Scope Swap
OpenAI said a Lean formalization backed its Navier-Stokes proof.
An arXiv paper finds the Lean code uses five extra derivatives where the written proof claims four.
OpenAI said its system produced a proof and a Lean formalization resolving the Navier-Stokes Millennium Prize problem.
Before you read on. Your call?
TRUE, BUT
Lean
A 6 October arXiv paper finds the Lean proof does not correspond to the written proof; in Lemma 8.6 the Lean code uses five additional derivatives, not four. The authors make no claim the written proof is wrong. The result also covers a fluid with a smooth force applied.
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The trick has a name
We call it Scope Swap: applies to far less than it sounds like. You'll see it again. Learn to spot it →
Receipts
- Supports web.archive.org:
This resolves the Navier–Stokes Millennium Prize problem by establishing statement “C” (and also “D”)
- Supports web.archive.org:
Our system produced an analytical proof and a Lean formalization that an initially smooth fluid at rest can develop a singularity
- Context web.archive.org:
The fluid has a smooth force applied to it
- Refutes arxiv.org:
we show that the formalised Lean proof does not correspond to the NL proof of blow-up of solutions to the Navier-Stokes equations
- Refutes arxiv.org:
the NL argument in Lemma 8.6 in the announced proof of blow-up of Navier–Stokes has not been faithfully translated into Lean
- Refutes arxiv.org:
all use five additional derivatives, not four
- Context arxiv.org:
The Lean code merely tells us that the theorem is correct
- Context arxiv.org:
We do not make claims about the correctness of OpenAI’s NL proof, we only make statements about mistranslations into Lean.
- Refutes tuftsdaily.com:
The result does not close the question, since Fefferman’s formulation sets the external force to
- Context tuftsdaily.com:
zero in one case while allowing a smooth force in the other.
- Context tuftsdaily.com:
OpenAI’s proof addresses the latter, leaving the behavior of a fluid that nothing pushes as an open problem.
- Context tuftsdaily.com:
a language that machine-checks each step of a proof
- Context tuftsdaily.com:
those agents exchanged 2.7 million messages and used about 130 billion tokens on this problem alone
Open the Receipts Pack → What each source proves, every figure traced, and what would change our verdict.
