{
  "id": "sampling-graphs-with-given-degrees",
  "title": "Sampling graphs with given degrees",
  "description": "OpenAI's proof (2026) that the switch chain on simple graphs with given degrees mixes in polynomial time for every graphical degree vector, through the operator inequality H^2 >= H for pair resamplings, and an exact uniform sampler with expected polynomial running time.",
  "units": [
    {
      "id": "the-switch-chain",
      "title": "The switch chain",
      "reader": "the-switch-chain.html",
      "source": "src/the-switch-chain.md",
      "source_sha256": "0aabe93bb2f74e614d30e4084fb090b65ce2287d2e2b2a6a7f66836cae152285",
      "status": "author_self_checked"
    },
    {
      "id": "a-variance-inequality-for-three-rows",
      "title": "A variance inequality for three rows",
      "reader": "a-variance-inequality-for-three-rows.html",
      "source": "src/a-variance-inequality-for-three-rows.md",
      "source_sha256": "26c22ef7d12c407f5047e8a8e80ca576fb761b9590b5f71b35af764408b4216c",
      "status": "author_self_checked"
    },
    {
      "id": "disjoint-pair-resamplings",
      "title": "Disjoint pair resamplings",
      "reader": "disjoint-pair-resamplings.html",
      "source": "src/disjoint-pair-resamplings.md",
      "source_sha256": "4a26cda98c6c81c905cb7ff05d85ff3a786ec6939032044ab7bbf7ce40458818",
      "status": "author_self_checked"
    },
    {
      "id": "exact-uniform-sampling",
      "title": "Exact uniform sampling",
      "reader": "exact-uniform-sampling.html",
      "source": "src/exact-uniform-sampling.md",
      "source_sha256": "7f4c5678c4c529295bf4ba976d10ac5a4fde5539d60340695e2a6a01d64e1198",
      "status": "author_self_checked"
    }
  ],
  "prerequisites": [],
  "status": "author_self_checked",
  "proof_providers": "providers.json",
  "provenance": "provenance.json",
  "licence": "CC0-1.0"
}