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        "title": "OpenAI, On the Navier–Stokes Millennium Prize Problem (8 Sep 2026; updated 10 Sep)",
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        "domain": "偏微分方程"
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          "url": "https://openai.com/index/navier-stokes-solution/"
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        {
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      "statement": "# OpenAI: candidate finite-time Navier–Stokes blow-up\n\nReports a three-dimensional, finite-energy blow-up construction driven by smooth forcing, corresponding to CMI formulations C/D.\n\n## Scientific scope\n\nWRS has not reviewed the proof or replayed Lean. Candidate status, source claims and the recorded CMI Active status remain separate. Do not attribute the work to an ordinary publicly released model.\n\n## Reading status\n\nThis is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.\n\n## People and systems\n\n\n\nListed source contributors; individual labor shares are not measured\n\nOpenAI research agents / OpenAI / Undisclosed internal model: Candidate proof generation (source reported).\n\nCodex / OpenAI / GPT-6 Astra: Subsequent Lean formalization; not the same attribution as the model generating the candidate proof (source reported).\n\n## Original sources\n\n- [OpenAI, On the Navier–Stokes Millennium Prize Problem (8 Sep 2026; updated 10 Sep)](https://openai.com/index/navier-stokes-solution/)\n- [Finite time blowup for Navier–Stokes, Theorem 1.1; §10, Corollary 10.6](https://cdn.openai.com/pdf/32d9f210-8b73-45e0-91bc-82a30aef8a9a/navier-stokes.pdf)\n- [CMI Navier–Stokes: Active](https://www.claymath.org/millennium/navier-stokes-equation/)\n- [CMI prize rules](https://www.claymath.org/millennium-problems/rules/)\n",
      "summary": "Reports a three-dimensional, finite-energy blow-up construction driven by smooth forcing, corresponding to CMI formulations C/D.",
      "title": "OpenAI: candidate finite-time Navier–Stokes blow-up"
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    "track": "Candidate mathematical result",
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    "evidence_summary": "The author announcement reports analytical and Lean work. These are source claims here, not a WRS replay or provider attestation.",
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        "locator": "The result; How we found the proof; September 10 update"
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