{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R649",
  "content_hash": null,
  "slug": "rdcr-claim-global-lower-bound-fourteen",
  "type": "claim",
  "title": "The requested maximum is at least fourteen",
  "summary": "A length-14 rainbow divisor-count interval is certified, and exhaustive search proves 14 is the exact maximum through endpoint \\(10^{10}\\); whether a longer interval ends between \\(10^{10}\\) and \\(10^{12}\\) remains open.",
  "relevance": "For Longest rainbow divisor-count interval below 10^12, record rdcr-claim-global-lower-bound-fourteen (“The requested maximum is at least fourteen”) records a bound, answer, status fact, or structural consequence. The record states: A length-14 rainbow divisor-count interval is certified, and exhaustive search proves 14 is the exact maximum through endpoint \\(10^{10}\\); whether a longer interval ends between \\(10^{10}\\) and \\(10^{12}\\) remains open.",
  "relevance_source": "recorded",
  "body": "The interval\n\\[\n1745175039\\leq n\\leq1745175052\n\\]\nhas divisor-count vector\n\\[\n(12,80,16,96,8,6,32,4,24,128,2,48,20,36).\n\\]\nAll fourteen entries are different. Its final integer is below \\(10^{12}\\), so the candidate's maximum \\(L\\) satisfies\n\\[\nL\\geq14.\n\\]\nThe companion sweep finds this as the first length-14 record. The global upper bound requested by the candidate remains open in this fixture because the exhaustive computation stops at \\(10^{10}\\).",
  "status": "supported",
  "evidence_grade": "reproduced",
  "scope": {
    "kind": "bounded",
    "statement": "the optimization over positive m and L satisfying m+L-1 <= 1000000000000",
    "bounds": {
      "interval_end": {
        "min": 1,
        "max": 1000000000000
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://arxiv.org/abs/1510.07081",
      "locator": "Exact factorization table in rdcr-claim-factorized-run and exhaustive computation in rdcr-artifact-segmented-prefix-sweep"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/1510.07081",
    "locator": "Exact factorization table in rdcr-claim-factorized-run and exhaustive computation in rdcr-artifact-segmented-prefix-sweep"
  },
  "relations": [
    {
      "slug": "R648",
      "title": "Exact factorizations certify the length-fourteen witness",
      "object_type": "claim",
      "relation": "supports",
      "direction": "incoming"
    },
    {
      "slug": "R650",
      "title": "Nearby literature treats different consecutive-divisor questions",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "rainbow-divisor-count-run-1e12",
      "title": "rainbow divisor count run 1e12",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}