{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R193",
  "content_hash": null,
  "slug": "dbm-artifact-determinants-130",
  "type": "artifact",
  "title": "Exact determinant sweep through order 130",
  "summary": "Bareiss elimination verifies the closed formula at every order through 130.",
  "relevance": "This supplies a computation, dataset, or executable check used to assess the target problem.",
  "relevance_source": "derived",
  "body": "Exact integer determinants agree with the formula for all \\(1\\leq n\\leq130\\). The 65 odd orders have determinant zero. Among the even orders, 33 determinants equal \\(-1\\) and 32 equal \\(1\\). This explains the original observation that exactly 65 of the first 130 determinants are nonzero: they are precisely the even orders.",
  "status": "available",
  "evidence_grade": "executable",
  "scope": {
    "kind": "bounded",
    "statement": "every matrix order from 1 through 130",
    "bounds": {
      "n": {
        "min": 1,
        "max": 130
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "partial",
    "kind": "python_computation",
    "source": "research/candidate-screening/verify.py",
    "citation": {
      "url": "https://github.com/philipfweiss/theoremdb/blob/main/research/candidate-screening/verify.py",
      "locator": "research/candidate-screening/verify.py and verified_ranges.json; formula independently checked on 2026-07-24"
    },
    "outputs": "research/candidate-screening/verified_ranges.json",
    "missing": [
      "command",
      "runtime"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://github.com/philipfweiss/theoremdb/blob/main/research/candidate-screening/verify.py",
    "locator": "research/candidate-screening/verify.py and verified_ranges.json; formula independently checked on 2026-07-24"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R194",
      "title": "Exact determinant of the disjoint-binary-support matrix",
      "object_type": "claim",
      "relation": "tests",
      "direction": "outgoing"
    },
    {
      "slug": "disjoint-binary-support-determinant",
      "title": "disjoint binary support determinant",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}