{
  "id": "shortest-common-superstrings",
  "title": "Shortest common superstrings",
  "description": "OpenAI's polynomial-time algorithm (2026) that finds a common superstring at most twice as long as the shortest one, for every finite family of strings. Forced occurrence counts give a balanced graph of cost at most the optimum; periodic layers and a rule for periodic words show how to connect it at no more than the same cost again.",
  "units": [
    {
      "id": "superstrings-and-the-hierarchical-graph",
      "title": "Superstrings and the hierarchical graph",
      "reader": "superstrings-and-the-hierarchical-graph.html",
      "source": "src/superstrings-and-the-hierarchical-graph.md",
      "source_sha256": "28343ed153a1a7cf5bd273656ee911e54c7302570a41e427d15694f1dad3ac40",
      "status": "author_self_checked"
    },
    {
      "id": "forced-occurrence-counts",
      "title": "Forced occurrence counts",
      "reader": "forced-occurrence-counts.html",
      "source": "src/forced-occurrence-counts.md",
      "source_sha256": "5ea64b359963fb2e1a4be887e6dce79997b2d5c762b84e53be4cd65ea3a71c05",
      "status": "author_self_checked"
    },
    {
      "id": "periodic-layers",
      "title": "Periodic layers",
      "reader": "periodic-layers.html",
      "source": "src/periodic-layers.md",
      "source_sha256": "43f881409ae33f5129598510bd6626cb37204edc5fc885b904fd249bfa47f222",
      "status": "author_self_checked"
    },
    {
      "id": "connecting-the-layers",
      "title": "Connecting the layers",
      "reader": "connecting-the-layers.html",
      "source": "src/connecting-the-layers.md",
      "source_sha256": "e4121c5a6708941cba5b8a47e3fb889edbaa1eb8f3d49f7c54b1615c75139790",
      "status": "author_self_checked"
    }
  ],
  "prerequisites": [],
  "status": "author_self_checked",
  "proof_providers": "providers.json",
  "provenance": "provenance.json",
  "licence": "CC0-1.0"
}