{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1495",
  "content_hash": null,
  "slug": "diagonal-ramsey-exponential-limit-claim-status-20260801",
  "type": "claim",
  "title": "Current status and exact unresolved remainder",
  "summary": "OPEN as checked on 2026-08-01. Strongest checked neighboring result: Current cited bounds give \\(\\sqrt2\\le\\liminf R(k)^{1/k}\\le\\limsup R(k)^{1/k}\\le3.7992\\ldots\\). Exact unresolved remainder: Even existence of the limit is unknown, as is its value.",
  "relevance": "This is the dated publication status for the canonical target Existence and value of the diagonal Ramsey exponential limit.",
  "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: Current cited bounds give \\(\\sqrt2\\le\\liminf R(k)^{1/k}\\le\\limsup R(k)^{1/k}\\le3.7992\\ldots\\).\n\nThe exact unresolved remainder is: Even existence of the limit is unknown, as is its value.\n\nA complete resolution must meet the following acceptance conditions:\n- Prove convergence of \\(R(k)^{1/k}\\) and identify the limit, or prove that the sequence has no limit.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://www.erdosproblems.com/77",
      "locator": "Thomas F. Bloom, Erdős Problem #77, Erdős Problems database (living entry), accessed 2026-08-01. Problem #77, OPEN banner, statement, remarks, and bibliography"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://www.erdosproblems.com/77",
    "locator": "Thomas F. Bloom, Erdős Problem #77, Erdős Problems database (living entry), accessed 2026-08-01. Problem #77, OPEN banner, statement, remarks, and bibliography"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R1494",
      "title": "Strongest checked neighboring result",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R1492",
      "title": "Dated source and duplicate audit",
      "object_type": "attempt",
      "relation": "evidences",
      "direction": "incoming"
    },
    {
      "slug": "R1493",
      "title": "Work at the unresolved boundary",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "diagonal-ramsey-exponential-limit",
      "title": "diagonal ramsey exponential limit",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}