{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R293",
  "content_hash": null,
  "slug": "fib-claim-lucas-generalization",
  "type": "claim",
  "title": "Lucas sequences may share total unimodularity",
  "summary": "Initial tests suggested the Fibonacci construction extends to Lucas sequences, including Lucas and Pell numbers.",
  "relevance": "For fib problem determinant range; fib problem nonzero support, record fib-claim-lucas-generalization (“Lucas sequences may share total unimodularity”) records a bound, answer, status fact, or structural consequence. The record states: Initial tests suggested the Fibonacci construction extends to Lucas sequences, including Lucas and Pell numbers.",
  "relevance_source": "recorded",
  "body": "Later examples show that recurrence growth alone cannot characterize the valid sequences.",
  "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 109-135"
    },
    "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 109-135"
  },
  "relations": [
    {
      "slug": "R306",
      "title": "The matrices may be totally unimodular",
      "object_type": "claim",
      "relation": "generalizes",
      "direction": "outgoing"
    },
    {
      "slug": "R297",
      "title": "Several non-Lucas sequences also pass initial tests",
      "object_type": "claim",
      "relation": "broadens",
      "direction": "incoming"
    },
    {
      "slug": "R307",
      "title": "Every Fibonacci-sum matrix is totally unimodular",
      "object_type": "claim",
      "relation": "generalizes",
      "direction": "outgoing"
    }
  ]
}