{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R919",
  "content_hash": null,
  "slug": "fib-claim-total-unimodular-review-pending-v2",
  "type": "claim",
  "title": "Every Fibonacci-sum matrix is totally unimodular",
  "summary": "Every square minor of every M_n has determinant in {-1,0,1}.",
  "relevance": "Keeps the stronger total-unimodularity argument under separate prose review while its exact determinant consequence is verified.",
  "relevance_source": "recorded",
  "body": "The recorded argument proves chordal bipartiteness and outerplanarity for the support graph, uses face parity to establish Camion's divisibility condition, and concludes that every square minor is signed or zero. Its exact determinant-range consequence is now verified in Lean. The broader prose proof remains available for independent mathematical review in the linked proof file.",
  "status": "supported",
  "evidence_grade": "mathematical_argument",
  "scope": {
    "kind": "universal",
    "statement": "every square minor of every matrix M_n, for 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": "Self-contained proof in 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": "Self-contained proof in research/fibonacci/total_unimodularity_proof.md"
  },
  "relations": [
    {
      "slug": "fib-problem-determinant-range",
      "title": "Fibonacci-sum indicator determinant conjecture",
      "object_type": "problem",
      "relation": "claims_resolution_of",
      "direction": "outgoing"
    },
    {
      "slug": "R918",
      "title": "The determinant is always minus one, zero, or one",
      "object_type": "claim",
      "relation": "strengthens",
      "direction": "outgoing"
    },
    {
      "slug": "R307",
      "title": "Every Fibonacci-sum matrix is totally unimodular",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "outgoing"
    }
  ]
}