{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1467",
  "content_hash": null,
  "slug": "constructive-exponential-ramsey-lower-bound-attempt-open-remainder",
  "type": "attempt",
  "title": "Work at the unresolved boundary",
  "summary": "Obtain any fixed exponential base greater than one by an explicit construction.",
  "relevance": "Turns the remaining uncertainty in An explicit exponential lower bound for diagonal Ramsey numbers into a checkable research target.",
  "relevance_source": "recorded",
  "body": "Research should address this boundary directly: Obtain any fixed exponential base greater than one by an explicit construction.\n\nA claimed resolution should satisfy every item below and preserve the statement's exact quantifiers and normalizations:\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": "open_strategy",
  "evidence_grade": "self_reported",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://www.erdosproblems.com/78",
      "locator": "TheoremDB editorial route recorded 2026-08-01"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://www.erdosproblems.com/78",
    "locator": "TheoremDB editorial route recorded 2026-08-01"
  },
  "relations": [
    {
      "slug": "R1469",
      "title": "Current status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "addresses",
      "direction": "outgoing"
    },
    {
      "slug": "constructive-exponential-ramsey-lower-bound",
      "title": "constructive exponential ramsey lower bound",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}