{
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  "ref": "R1468",
  "content_hash": null,
  "slug": "constructive-exponential-ramsey-lower-bound-claim-literature-frontier",
  "type": "claim",
  "title": "Strongest checked neighboring result",
  "summary": "The maintained record gives explicit constructions whose largest clique or independent set is at most \\((\\log n)^C\\), which remains too large to yield \\(N_k\\ge C_0^k\\).",
  "relevance": "Locates the present research frontier immediately below An explicit exponential lower bound for diagonal Ramsey numbers.",
  "relevance_source": "recorded",
  "body": "The maintained record gives explicit constructions whose largest clique or independent set is at most \\((\\log n)^C\\), which remains too large to yield \\(N_k\\ge C_0^k\\).\n\nThis leaves the following boundary unresolved: Obtain any fixed exponential base greater than one by an explicit construction. The distinction is retained here so a restricted theorem, finite computation, or neighboring case is not presented as a solution of the full target.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://www.erdosproblems.com/78",
      "locator": "Thomas F. Bloom, Erdős Problem #78, Erdős Problems database (living entry), accessed 2026-08-01. Problem #78, OPEN banner, statement, remarks, and bibliography"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://www.erdosproblems.com/78",
    "locator": "Thomas F. Bloom, Erdős Problem #78, Erdős Problems database (living entry), accessed 2026-08-01. Problem #78, OPEN banner, statement, remarks, and bibliography"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R1469",
      "title": "Current status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "constructive-exponential-ramsey-lower-bound",
      "title": "constructive exponential ramsey lower bound",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}