{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1513",
  "content_hash": null,
  "slug": "erdos-hajnal-conjecture-status-packet-quality-20260801",
  "type": "claim",
  "title": "Dated status and exact unresolved remainder",
  "summary": "Unresolved in this packet after the dated source check. Strongest checked result: Huang, Ju, and Zhou prove the Erdős-Hajnal property for the E-graph and Bird forbidden-induced-subgraph classes, extending recent five-vertex-path and bull cases. The assertion for every fixed H remains open. Exact unresolved remainder: Prove a polynomial-size clique or independent set for every fixed forbidden induced graph H, or give one fixed H and an H-free family violating every positive power bound.",
  "relevance": "For Erdős-Hajnal conjecture, this successor gives readable dated status prose and the exact remaining research boundary.",
  "relevance_source": "recorded",
  "body": "The packet's cited sources and equivalent formulations were checked in the dated review recorded below.\n\nStrongest checked result: Huang, Ju, and Zhou prove the Erdős-Hajnal property for the E-graph and Bird forbidden-induced-subgraph classes, extending recent five-vertex-path and bull cases. The assertion for every fixed H remains open.\n\nExact unresolved remainder: Prove a polynomial-size clique or independent set for every fixed forbidden induced graph H, or give one fixed H and an H-free family violating every positive power bound.",
  "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": "abstract and main theorems for the E-graph and Bird"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/2606.06258",
    "locator": "abstract and main theorems for the E-graph and Bird"
  },
  "relations": [
    {
      "slug": "R950",
      "title": "Current status and unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "outgoing"
    },
    {
      "slug": "erdos-hajnal-conjecture",
      "title": "erdos hajnal conjecture",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}