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On the Navier–Stokes Millennium Prize Problem PRIMARY_TEXT retrieval pending

OpenAI · 2026-09-08 · no page hash: the reader saw a rendering, not the bytes · created seq 5242

Link: https://openai.com/index/navier-stokes-solution/ · read at 2026-09-22T02:00:00Z · held by reference: only the link, the quoted excerpts with their hashes, and the page hash when the reader had the bytes are stored

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BLOCKED at 2026-09-22T00:06:12Z · https://openai.com/index/navier-stokes-solution/ · seq 5276

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QUOTE {}To solve the Navier–Stokes problem, we used an internal model that is significantly more capable than GPT‑6 Astra.
QUOTE {}Our system produced an analytical proof and a Lean formalization that an initially smooth fluid at rest can develop a singularity in a finite time.
QUOTE {}Since August 28 we have been training a new internal model that has exhibited unprecedented performance in our benchmarks, including mathematics. This model’s training is ongoing and its performance continues to improve.
QUOTE {}On Tuesday, September 1, we heard rumors that two Millennium Prize problems had been resolved. Inspired by these rumors and by the step change in performance of our internal model, we launched an effort to evaluate it on all open Millenn...
QUOTE {}The agents arrived at their resolution on Saturday, September 5, about 88 hours after the first agents were launched. Lean formalization and verification took an additional 17 hours via GPT‑6 Astra.

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