{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R309",
  "content_hash": null,
  "slug": "fib-claim-unimodular-review-pending",
  "type": "claim",
  "title": "Every nonsingular Fibonacci-sum matrix is unimodular",
  "summary": "For every n, the determinant of M_n is 0, 1, or -1.",
  "relevance": "For fib problem determinant range; fib problem nonzero support, record fib-claim-unimodular-review-pending (“Every nonsingular Fibonacci-sum matrix is unimodular”) records a bound, answer, status fact, or structural consequence. The record states: For every n, the determinant of M_n is 0, 1, or -1.",
  "relevance_source": "recorded",
  "body": "This follows immediately if the recorded total-unimodularity argument passes independent review.",
  "status": "supported",
  "evidence_grade": "mathematical_argument",
  "scope": {
    "kind": "universal",
    "statement": "every matrix size n >= 1"
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://mathoverflow.net/questions/513340/is-the-determinant-of-this-fibonacci-sum-indicator-matrix-always-1-0-or/513372",
      "locator": "research/fibonacci/total_unimodularity_proof.md"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://mathoverflow.net/questions/513340/is-the-determinant-of-this-fibonacci-sum-indicator-matrix-always-1-0-or/513372",
    "locator": "research/fibonacci/total_unimodularity_proof.md"
  },
  "relations": [
    {
      "slug": "fib-problem-determinant-range",
      "title": "Fibonacci-sum indicator determinant conjecture",
      "object_type": "problem",
      "relation": "strengthens",
      "direction": "outgoing"
    },
    {
      "slug": "R918",
      "title": "The determinant is always minus one, zero, or one",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "incoming"
    },
    {
      "slug": "R307",
      "title": "Every Fibonacci-sum matrix is totally unimodular",
      "object_type": "claim",
      "relation": "strengthens",
      "direction": "incoming"
    },
    {
      "slug": "R308",
      "title": "The full matrix may be unimodular",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "outgoing"
    }
  ]
}