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Benefit Ledger · disputed · Mathematics

OpenAI claims a forced Navier–Stokes singularity from an unreleased system

On 8 September 2026 OpenAI published a 166-page writeup and Lean formalization arguing that smooth, finite-energy 3D Navier–Stokes dynamics with a smooth external force can blow up in finite time, which it says settles Clay statements C and D. The search model was an unreleased internal system; GPT-6 Astra did the Lean step.

8 Sep 2026Tier 3 MajorMethodology 0.1

Current score

+1.13

10 base · Major (tier 3 of 5, 10 pts)
× 0.9000 attribution · Primary causal contribution
× 0.4500 evidence · External expert evaluation
× 0.4500 realization · Experimentally validated
× 0.6500 durability
Event-level product before credit split: 1.18

A Clay C/D Navier–Stokes singularity would be historic if accepted; until independent reconstruction and CMI evaluation it is scored as major (tier 3) and disputed. Search credit goes to the unreleased system (0.85 share), with Astra only for Lean (0.15). Evidence is announcement plus Lean plus Nature/CMI commentary, not peer review (0.45). Realization is a public manuscript, not community acceptance (0.45).

What happened

OpenAI reports that after rumors on 1 September 2026 that other researchers had resolved Millennium problems, it launched a multi-agent evaluation of an internal model still in training and more capable than GPT-6 Astra. About 10,000 concurrent agents ran on Navier–Stokes; OpenAI says they reached a resolution on 5 September after roughly 88 hours, then Astra spent about 17 hours on Lean formalization (complete 6 September). The claimed theorem is finite-time blowup for an initially smooth fluid at rest, with a smooth force and bounded energy, matching Fefferman’s statements C and D rather than the unforced problem many analysts treat as the essential question. OpenAI says it will not claim the Clay prize. The Clay Mathematics Institute wrote on 11 September that the problem has ‘apparently been settled’ while stressing an unhurried evaluation. Nature covered the claim as a company announcement. Tristan Buckmaster alleges OpenAI moved after learning of his work with Levent Alpöge; OpenAI says the proofs differ (forced Navier–Stokes vs their forced Euler/IPM/Boussinesq program) and that it did not see their manuscripts. Hodge, Birch–Swinnerton-Dyer, Riemann, Yang–Mills, and P vs NP are not recorded as solved. This event is disputed: lab-published and Lean-accompanied, not independently reconstructed, not prize-awarded, and contested on both the forced formulation and priority.

Model attribution

GPT-6

Unreleased multi-agent system OpenAI says produced the analytic Navier–Stokes singularity.

OpenAI attributes the proof search to an internal model significantly more capable than GPT-6 Astra, not to the public Astra release.

Attribution 0.9000 · Credit share 85% · OpenAI

GPT-6

Named release used for the 17-hour Lean formalization and verification pass after the internal system produced the analytic argument.

OpenAI credits Astra with Lean formalization, not with finding the Navier–Stokes argument.

Attribution 0.6000 · Credit share 15% · OpenAI

Claims

  • OpenAI published a paper and Lean artifact claiming finite-time blowup for forced 3D incompressible Navier–Stokes with smooth data and bounded energy, corresponding to Clay statements C and D.

    outcome · supported

  • The Clay Mathematics Institute has awarded the Millennium Prize or completed its evaluation.

    significance · disputed

  • GPT-6 Astra produced the Navier–Stokes proof.

    attribution · disputed

  • Hodge, Birch–Swinnerton-Dyer, Riemann, Yang–Mills, or P vs NP have been solved in the same week.

    significance · disputed

Sources

primary sources

independent sources

Secondary domains: Physics, Computer Science

Revision history

  • 13 Sep 2026 · 0.00 1.13

    Imported September 2026 mathematics events under methodology 0.1 credit-unit rules.

OpenAI claims a forced Navier–Stokes singularity from an unreleased system · NetGoodIndex