{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R950",
  "content_hash": null,
  "slug": "erdos-hajnal-conjecture-claim-status-20260731",
  "type": "claim",
  "title": "Current status and unresolved remainder",
  "summary": "The cited 2026 paper proves new cases of the Erdős-Hajnal conjecture while treating the general assertion as open. The source and public status were checked on 2026-07-31. This is an admin-curated seed record, not an independent exhaustive literature review. Prove the polynomial-size homogeneous-set bound for every fixed forbidden induced graph H, or give a fixed H and an infinite family of H-free graphs whose largest cliques and independent sets are smaller than n^c for every positive c.",
  "relevance": "Defines the dated frontier and the exact remainder that research on this problem must resolve.",
  "relevance_source": "recorded",
  "body": "The cited 2026 paper proves new cases of the Erdős-Hajnal conjecture while treating the general assertion as open. The source and public status were checked on 2026-07-31. This is an admin-curated seed record, not an independent exhaustive literature review.\n\nA complete resolution must satisfy this condition: Prove the polynomial-size homogeneous-set bound for every fixed forbidden induced graph H, or give a fixed H and an infinite family of H-free graphs whose largest cliques and independent sets are smaller than n^c for every positive c.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://arxiv.org/abs/2606.06258",
      "locator": "See dataset.references[0] for the exact external source and locator."
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/2606.06258",
    "locator": "See dataset.references[0] for the exact external source and locator."
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R949",
      "title": "Resolve the stated acceptance condition",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "R1513",
      "title": "Dated status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "incoming",
      "metadata": {
        "reason": "Replaces unreadable status prose with the dated review from 2026-08-01."
      }
    },
    {
      "slug": "erdos-hajnal-conjecture",
      "title": "erdos hajnal conjecture",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}