{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1469",
  "content_hash": null,
  "slug": "constructive-exponential-ramsey-lower-bound-claim-status-20260801",
  "type": "claim",
  "title": "Current status and exact unresolved remainder",
  "summary": "OPEN as checked on 2026-08-01. Strongest checked neighboring result: 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\\). Exact unresolved remainder: Obtain any fixed exponential base greater than one by an explicit construction.",
  "relevance": "This is the dated publication status for the canonical target An explicit exponential lower bound for diagonal Ramsey numbers.",
  "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: 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\nThe exact unresolved remainder is: Obtain any fixed exponential base greater than one by an explicit construction.\n\nA complete resolution must meet the following acceptance conditions:\n- Specify the construction, prove it avoids monochromatic \\(K_k\\), and prove \\(N_k\\ge C^k\\) for a fixed \\(C>1\\) on an infinite sequence of \\(k\\).",
  "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"
  },
  "relations": [
    {
      "slug": "R1468",
      "title": "Strongest checked neighboring result",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R1466",
      "title": "Dated source and duplicate audit",
      "object_type": "attempt",
      "relation": "evidences",
      "direction": "incoming"
    },
    {
      "slug": "R1467",
      "title": "Work at the unresolved boundary",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "constructive-exponential-ramsey-lower-bound",
      "title": "constructive exponential ramsey lower bound",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
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}