{
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  "ref": "R1581",
  "content_hash": null,
  "slug": "graph-isomorphism-in-p-claim-status-20260801",
  "type": "claim",
  "title": "Current status and exact unresolved remainder",
  "summary": "OPEN as checked on 2026-08-01. Strongest checked neighboring result: Babai's deterministic quasipolynomial-time algorithm is the best general worst-case bound located. Exact unresolved remainder: A polynomial-time bound remains open.",
  "relevance": "This is the dated publication status for the canonical target Is graph isomorphism solvable in polynomial time?.",
  "relevance_source": "recorded",
  "body": "The problem was checked as open on 2026-08-01.\n\nThe strongest neighboring result found in the cited sources is: Babai's deterministic quasipolynomial-time algorithm is the best general worst-case bound located.\n\nThe exact unresolved remainder is: A polynomial-time bound remains open.\n\nA complete resolution must meet the following acceptance conditions:\n- Give and prove a deterministic polynomial-time isomorphism algorithm.\n- Or prove no such algorithm exists in a stated standard model, which would separate complexity classes.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://doi.org/10.1145/2897518.2897542",
      "locator": "L. Babai, Graph isomorphism in quasipolynomial time, STOC 2016. main theorem"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1145/2897518.2897542",
    "locator": "L. Babai, Graph isomorphism in quasipolynomial time, STOC 2016. main theorem"
  },
  "relations": [
    {
      "slug": "R1580",
      "title": "Strongest checked neighboring result",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R1578",
      "title": "Dated source and duplicate audit",
      "object_type": "attempt",
      "relation": "evidences",
      "direction": "incoming"
    },
    {
      "slug": "R1579",
      "title": "Work at the unresolved boundary",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "graph-isomorphism-in-p",
      "title": "graph isomorphism in p",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
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}