{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R752",
  "content_hash": null,
  "slug": "ssm34-claim-certified-interval",
  "type": "claim",
  "title": "The maximum is between 35^16 and 6,876,227,375,063^2",
  "summary": "A principal submatrix of a skew conference matrix gives the lower endpoint, while the skew Ehlich-Wojtas bound and Pfaffian integrality give the upper endpoint.",
  "relevance": "For Maximum determinant of a skew Seidel matrix of order 34, record ssm34-claim-certified-interval (“The maximum is between 35^16 and 6,876,227,375,063^2”) records a bound, answer, status fact, or structural consequence. The record states: A principal submatrix of a skew conference matrix gives the lower endpoint, while the skew Ehlich-Wojtas bound and Pfaffian integrality give the upper endpoint.",
  "relevance_source": "recorded",
  "body": "Write \\(D_{34}\\) for the requested maximum. The certified bounds are\n\\[\n5{,}070{,}942{,}774{,}902{,}496{,}337{,}890{,}625\n =35^{16}\n \\leq D_{34}\n \\leq 6{,}876{,}227{,}375{,}063^2\n =47{,}282{,}502{,}913{,}565{,}795{,}274{,}253{,}969.\n\\]\nThe lower endpoint is attained by the explicit order-34 matrix in `ssm34-artifact-gs36-principal-minor`. The upper endpoint follows for every matrix in the stated family. These sources and the computation do not determine equality at either endpoint, so the exact maximum remains open in this entry.",
  "status": "supported",
  "evidence_grade": "reproduced",
  "scope": {
    "kind": "bounded",
    "statement": "all 34 by 34 skew-symmetric matrices with zero diagonal and every off-diagonal entry in {-1,1}",
    "bounds": {
      "matrix_order": {
        "min": 34,
        "max": 34
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://arxiv.org/abs/2406.09697",
      "locator": "Klanderman, Montee, Piotrowski, Rice, and Shader, Theorems 5.4 and 5.5, combined with the order-36 construction of Goethals and Seidel and the exact replay below"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/2406.09697",
    "locator": "Klanderman, Montee, Piotrowski, Rice, and Shader, Theorems 5.4 and 5.5, combined with the order-36 construction of Goethals and Seidel and the exact replay below"
  },
  "relations": [
    {
      "slug": "R753",
      "title": "An explicit order-34 matrix has determinant 35^16",
      "object_type": "claim",
      "relation": "supports",
      "direction": "incoming"
    },
    {
      "slug": "R754",
      "title": "Every determinant is at most 6,876,227,375,063^2",
      "object_type": "claim",
      "relation": "supports",
      "direction": "incoming"
    },
    {
      "slug": "skew-seidel-maxdet-34",
      "title": "skew seidel maxdet 34",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}