{
  "id": "polynomial-removal-fails-for-ordered-matrices",
  "title": "Polynomial removal fails for ordered binary matrices",
  "description": "OpenAI's counterexample (2026) to polynomial removal for ordered binary matrices: a fixed 66 x 66 pattern and tree-indexed matrices that are far from avoiding it but contain very few copies of it.",
  "units": [
    {
      "id": "ordered-copies-and-tree-matrices",
      "title": "Ordered copies and tree matrices",
      "reader": "ordered-copies-and-tree-matrices.html",
      "source": "src/ordered-copies-and-tree-matrices.md",
      "source_sha256": "520d1b01b2bf9adef2fe857f0354ca2243c77309b87f3324802cfbf8f97fbf8b",
      "status": "author_self_checked"
    },
    {
      "id": "every-copy-meets-the-leaf-diagonal",
      "title": "Every copy meets the leaf diagonal",
      "reader": "every-copy-meets-the-leaf-diagonal.html",
      "source": "src/every-copy-meets-the-leaf-diagonal.md",
      "source_sha256": "cbeb5f962fc57b40b74f0301ca8b146334a3271c337f72b0fc16195a1a6bbb84",
      "status": "author_self_checked"
    },
    {
      "id": "distance-from-freeness",
      "title": "Distance from freeness",
      "reader": "distance-from-freeness.html",
      "source": "src/distance-from-freeness.md",
      "source_sha256": "33682066a247661a522ba560017393de85ffa561c95d220eef5ee79cac55c483",
      "status": "author_self_checked"
    }
  ],
  "prerequisites": [],
  "status": "author_self_checked",
  "proof_providers": "providers.json",
  "provenance": "provenance.json",
  "licence": "CC0-1.0"
}