{
  "id": "superexponential-van-der-waerden-numbers",
  "title": "Superexponential van der Waerden numbers",
  "description": "OpenAI's theorem (2026) that van der Waerden numbers grow super-exponentially for every number of colours, W_r(k) > k^(ck floor(log2 r)); through circle coordinates and adaptive meshes, a balanced colouring chosen by the local lemma, and a sparse perturbation by squared-norm bands.",
  "units": [
    {
      "id": "van-der-waerden-numbers",
      "title": "Van der Waerden numbers",
      "reader": "van-der-waerden-numbers.html",
      "source": "src/van-der-waerden-numbers.md",
      "source_sha256": "38c7f88a6244f6514925941b082c36fde37e88203827a61eebe5472a472d31e7",
      "status": "author_self_checked"
    },
    {
      "id": "arrangements-tails-and-the-local-lemma",
      "title": "Arrangements, tails and the local lemma",
      "reader": "arrangements-tails-and-the-local-lemma.html",
      "source": "src/arrangements-tails-and-the-local-lemma.md",
      "source_sha256": "530dd0c2a45cdc12492c3b5bdaf83437c06fa4cbfcae43a5355b786f43f8e0a6",
      "status": "author_self_checked"
    },
    {
      "id": "coordinates-meshes-and-label-counts",
      "title": "Coordinates, meshes and label counts",
      "reader": "coordinates-meshes-and-label-counts.html",
      "source": "src/coordinates-meshes-and-label-counts.md",
      "source_sha256": "e15ee1cb629ca2ebf489ca3baec76963659c672091f814e647fa44354e969672",
      "status": "author_self_checked"
    },
    {
      "id": "a-balanced-colouring-and-the-dichotomy",
      "title": "A balanced colouring and the dichotomy",
      "reader": "a-balanced-colouring-and-the-dichotomy.html",
      "source": "src/a-balanced-colouring-and-the-dichotomy.md",
      "source_sha256": "83e04a250fdb58d8e636948faf48d33b1e52462f3342c6ece3fb28ffb40d3b9d",
      "status": "author_self_checked"
    },
    {
      "id": "norm-bands-and-the-two-colouring",
      "title": "Norm bands and the two-colouring",
      "reader": "norm-bands-and-the-two-colouring.html",
      "source": "src/norm-bands-and-the-two-colouring.md",
      "source_sha256": "b963beb4e0b6b5bf60521fe03e77e56699015e5b99ce626e53df3556ffc19ebf",
      "status": "author_self_checked"
    }
  ],
  "prerequisites": [],
  "status": "author_self_checked",
  "proof_providers": "providers.json",
  "provenance": "provenance.json",
  "licence": "CC0-1.0"
}