[
  {
    "id": "openai-2026-09-21",
    "org": "OpenAI",
    "date": "2026-09-21",
    "title": "Advisory Group on Mathematics and Artificial Intelligence",
    "url": "https://openai.com/index/advisory-group-on-mathematics-and-ai/",
    "claimed": 100,
    "claimed_text": "more than 100 long-standing open problems across most areas of mathematics",
    "identified": 0,
    "written": 0,
    "checkable": 0,
    "nodes": [],
    "note": "Announced with an independent advisory group to advise on how the results should be released. None of the problems has been named.",
    "sources": [
      {
        "label": "OpenAI",
        "url": "https://openai.com/index/advisory-group-on-mathematics-and-ai/"
      },
      {
        "label": "TechCrunch",
        "url": "https://techcrunch.com/2026/09/21/openai-forms-math-advisory-group-as-its-ai-resolves-more-than-100-open-problems/"
      }
    ],
    "disclosure": "D0"
  },
  {
    "id": "openai-2026-09-08",
    "org": "OpenAI",
    "date": "2026-09-08",
    "title": "On the Navier–Stokes Millennium Prize Problem",
    "url": "https://openai.com/index/navier-stokes-solution/",
    "claimed": 2,
    "claimed_text": "Navier–Stokes blowup with smooth forcing, and unforced Euler blowup",
    "identified": 2,
    "written": 2,
    "checkable": 2,
    "nodes": [
      {
        "id": "millennium:NavierStokes",
        "label": "Existence And Smoothness Of The Navier–Stokes Equation",
        "page": "s/millennium-navierstokes",
        "verified": false,
        "checked_by": []
      }
    ],
    "note": "Both results carry a paper and a Lean formalisation checked with Comparator.",
    "sources": [
      {
        "label": "OpenAI",
        "url": "https://openai.com/index/navier-stokes-solution/"
      },
      {
        "label": "Lean formalisation",
        "url": "https://github.com/openai/NavierStokesAndEuler"
      }
    ],
    "disclosure": "D3"
  },
  {
    "id": "buckmaster-alpoge-2026-09-07",
    "org": "Tristan Buckmaster and Levent Alpöge",
    "date": "2026-09-07",
    "title": "Finite-time blowup with smooth forcing for porous media, Boussinesq and Euler",
    "url": "https://cims.nyu.edu/~tristanb/statement.pdf",
    "claimed": 4,
    "claimed_text": "three blowup results with smooth forcing, and blowup for hypodissipative Navier–Stokes held back until its Lean verification finishes",
    "identified": 4,
    "written": 3,
    "checkable": 0,
    "nodes": [
      {
        "id": "pde:EulerSmoothForcingBlowup",
        "label": "Finite-time blowup for the 3D incompressible Euler equations with smooth forcing",
        "page": "s/pde-eulersmoothforcingblowup",
        "verified": false,
        "checked_by": []
      },
      {
        "id": "pde:BoussinesqSmoothForcingBlowup",
        "label": "Finite-time blowup for the inviscid Boussinesq equations with smooth forcing",
        "page": "s/pde-boussinesqsmoothforcingblowup",
        "verified": false,
        "checked_by": []
      },
      {
        "id": "pde:PorousMediaSmoothForcingBlowup",
        "label": "Finite-time blowup for the incompressible porous media equation with smooth forcing",
        "page": "s/pde-porousmediasmoothforcingblowup",
        "verified": false,
        "checked_by": []
      }
    ],
    "note": "Three papers are public. The authors say the results were verified in Lean but cite no public repository, and the fourth result has no write-up yet.",
    "sources": [
      {
        "label": "Tristan Buckmaster, statement of 7 September 2026",
        "url": "https://cims.nyu.edu/~tristanb/statement.pdf"
      },
      {
        "label": "Terence Tao, on the three blowup results",
        "url": "https://terrytao.wordpress.com/2026/09/07/finite-time-blowup-with-smooth-forcing-term-for-the-incompressible-porous-medium-boussinesq-and-incompressible-euler-equations/"
      }
    ],
    "disclosure": "D1"
  },
  {
    "id": "anthropic-2026-09-04",
    "org": "Anthropic",
    "date": "2026-09-04",
    "title": "Formalizing Fermat's Last Theorem",
    "url": "https://www.anthropic.com/research/formalizing-fermats-last-theorem",
    "claimed": 1,
    "claimed_text": "a complete formalisation of Fermat's Last Theorem",
    "identified": 1,
    "written": 1,
    "checkable": 1,
    "nodes": [
      {
        "id": "mathlib:FermatLastTheorem",
        "label": "Fermat's Last Theorem",
        "page": "s/mathlib-fermatlasttheorem",
        "verified": false,
        "checked_by": []
      }
    ],
    "note": "The repository publishes the development, a Comparator challenge and a formalization.yaml.",
    "sources": [
      {
        "label": "Anthropic",
        "url": "https://www.anthropic.com/research/formalizing-fermats-last-theorem"
      },
      {
        "label": "Lean formalisation",
        "url": "https://github.com/anthropics/fermats-last-theorem"
      }
    ],
    "disclosure": "D3"
  },
  {
    "id": "anthropic-2026-08-10",
    "org": "Anthropic",
    "date": "2026-08-10",
    "title": "Learning more about Claude's mathematical capabilities",
    "url": "https://www.anthropic.com/research/riemann-zeta",
    "claimed": 1,
    "claimed_text": "a higher proven proportion of zeta zeros on the critical line",
    "identified": 1,
    "written": 1,
    "checkable": 1,
    "nodes": [
      {
        "id": "zeta:critical-line-proportion",
        "label": "Proportion of zeta zeros proved to lie on the critical line",
        "page": "t/zeta-critical-line-proportion",
        "verified": true,
        "checked_by": [
          "qed.bot"
        ]
      }
    ],
    "note": "A paper on arXiv and a Lean formalisation, rebuilt here.",
    "sources": [
      {
        "label": "Anthropic",
        "url": "https://www.anthropic.com/research/riemann-zeta"
      },
      {
        "label": "arXiv:2608.13637",
        "url": "https://arxiv.org/abs/2608.13637"
      }
    ],
    "disclosure": "D3"
  },
  {
    "id": "openai-2026-08-01",
    "org": "OpenAI",
    "date": "2026-08-01",
    "title": "Ten advances on open problems",
    "url": "https://github.com/openai/ten-proofs",
    "claimed": 10,
    "claimed_text": "ten advances on open problems in mathematics and theoretical computer science",
    "identified": 10,
    "written": 10,
    "checkable": 10,
    "nodes": [
      {
        "id": "erdos:146",
        "label": "Erdős Problem 146",
        "page": "s/erdos-146",
        "verified": true,
        "checked_by": [
          "qed.bot"
        ]
      },
      {
        "id": "erdos:183",
        "label": "Erdős Problem 183",
        "page": "s/erdos-183",
        "verified": true,
        "checked_by": [
          "qed.bot"
        ]
      }
    ],
    "note": "Each result is published with a Lean certificate. Two attach to Erdős problems held here, and both were rebuilt here.",
    "sources": [
      {
        "label": "openai/ten-proofs",
        "url": "https://github.com/openai/ten-proofs"
      }
    ],
    "disclosure": "D3"
  }
]