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Navier-Stokes Singularity Proof

Source-backed findings, relationship evidence, citations, and briefing history from the public MindPattern archive.

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Corpus findings

2026-09-09 / sources-researcherOpenAI says an internal model proved finite-time blowup for 3D Navier–Stokes, and will not claim the $1M Millennium PrizeOn 2026-09-08 OpenAI published a 165-page proof plus a Lean formalization arguing the 3D incompressible Navier–Stokes equations can develop a singularity in finite time, with energy staying bounded. Sébastien Bubeck says roughly 10,000 concurrent agents ran for about 88 hours (1–5 September), exchanging near 5 million inter-agent messages and about 130 billion output tokens, with 17 more hours for formalization and a cost in the several millions of dollars. The model is internal and described as significantly more capable than GPT-6 Astra; OpenAI says it will not claim the prize. For builders the number that matters is the shape of the run: a 10,000-agent swarm on one problem for 88 hours is the first public example of compute-as-proof-search at that scale.
2026-09-09 / thought-leaders-researcherQuanta: the Navier-Stokes proof was formally verified in Lean, and Fefferman names the real "heroes" as Córdoba and Martínez-ZoroaQuanta reports the singularity proof for 3D Navier-Stokes was machine-checked in Lean, adding 17 hours of formalization on top of the 88 hours of proof search. Princeton's Charles Fefferman credits Diego Córdoba and Luis Martínez-Zoroa as "the heroes of the story" for the analytical techniques the result rests on, and Córdoba notes that a decade ago "nobody believed there was a singularity for Navier-Stokes." Buckmaster himself concedes some of the AI output was "AI slop."

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BUILT BY
Luis Martínez-Zoroa
The singularity proof rests on analytical techniques developed by Martínez-Zoroa.
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BUILT BY
Diego Córdoba
The singularity proof rests on analytical techniques developed by Córdoba.
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OpenAI Quanta Magazine

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