{
  "id": "the-lane-emden-conjecture",
  "title": "The Lane-Emden conjecture",
  "description": "OpenAI's proof (2026) of the Lane-Emden conjecture and its weighted Henon-Lane-Emden form: below the critical hyperbola the elliptic system has no positive solution on R^n, without any condition at infinity, by a localized virial identity for Newton potentials and a comparison along parallel lines.",
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      "id": "spherical-means-and-newton-potentials",
      "title": "Spherical means and Newton potentials",
      "reader": "spherical-means-and-newton-potentials.html",
      "source": "src/spherical-means-and-newton-potentials.md",
      "source_sha256": "1a54766d59f11c2c2391aa77b0a775b083f5880676e2db53245deb40293ae154",
      "status": "author_self_checked"
    },
    {
      "id": "positive-solutions-and-their-potentials",
      "title": "Positive solutions and their potentials",
      "reader": "positive-solutions-and-their-potentials.html",
      "source": "src/positive-solutions-and-their-potentials.md",
      "source_sha256": "c8563dbc9dcdb34cd13e84f798efb01eda547942519bac08c0b3666e587d0448",
      "status": "author_self_checked"
    },
    {
      "id": "a-localized-virial-identity",
      "title": "A localized virial identity",
      "reader": "a-localized-virial-identity.html",
      "source": "src/a-localized-virial-identity.md",
      "source_sha256": "15c51f5ef7fdc692291d9fa6341e4645c748fd7b65076cb411e8429aa119b58a",
      "status": "author_self_checked"
    },
    {
      "id": "intervals-and-source-layers",
      "title": "Intervals and source layers",
      "reader": "intervals-and-source-layers.html",
      "source": "src/intervals-and-source-layers.md",
      "source_sha256": "4a5918d558703a67e61feb68d2fe70a6d37222023fabf688c0eb0e25204fde3d",
      "status": "author_self_checked"
    },
    {
      "id": "pressure-and-the-energy-bound",
      "title": "Pressure and the energy bound",
      "reader": "pressure-and-the-energy-bound.html",
      "source": "src/pressure-and-the-energy-bound.md",
      "source_sha256": "be3a11eb358ec46b7e899073fa0df90f2cbf85d4ea760d23bdb96dd939252067",
      "status": "author_self_checked"
    }
  ],
  "prerequisites": [],
  "status": "author_self_checked",
  "proof_providers": "providers.json",
  "provenance": "provenance.json",
  "licence": "CC0-1.0"
}