{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R306",
  "content_hash": null,
  "slug": "fib-claim-total-unimodular",
  "type": "claim",
  "title": "The matrices may be totally unimodular",
  "summary": "Random minor tests suggested that every square minor of M_n has determinant in {-1,0,1}.",
  "relevance": "For fib problem determinant range; fib problem nonzero support, record fib-claim-total-unimodular (“The matrices may be totally unimodular”) records a bound, answer, status fact, or structural consequence. The record states: Random minor tests suggested that every square minor of M_n has determinant in {-1,0,1}.",
  "relevance_source": "recorded",
  "body": "Total unimodularity would immediately imply the determinant conjecture and would demand a stronger structural explanation.",
  "status": "conjectured",
  "evidence_grade": "self_reported",
  "scope": null,
  "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": "comment lines 109-124"
    },
    "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": "comment lines 109-124"
  },
  "relations": [
    {
      "slug": "R308",
      "title": "The full matrix may be unimodular",
      "object_type": "claim",
      "relation": "strengthens",
      "direction": "outgoing"
    },
    {
      "slug": "R293",
      "title": "Lucas sequences may share total unimodularity",
      "object_type": "claim",
      "relation": "generalizes",
      "direction": "incoming"
    },
    {
      "slug": "R280",
      "title": "Prove total unimodularity",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "R307",
      "title": "Every Fibonacci-sum matrix is totally unimodular",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "incoming"
    }
  ]
}