{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R276",
  "content_hash": null,
  "slug": "fib-attempt-signed-matchings",
  "type": "attempt",
  "title": "Use the signed perfect-matching graph",
  "summary": "Treat M_n as a bipartite adjacency matrix and study cancellation among perfect matchings through alternating cycles.",
  "relevance": "For fib problem determinant range; fib problem nonzero support, record fib-attempt-signed-matchings (“Use the signed perfect-matching graph”) documents a concrete method, search boundary, or failed route. The record states: Treat M_n as a bipartite adjacency matrix and study cancellation among perfect matchings through alternating cycles.",
  "relevance_source": "recorded",
  "body": "A canonical alternating cycle could generate a sign-reversing matching involution.",
  "status": "open_strategy",
  "evidence_grade": "proposed",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://mathoverflow.net/questions/513340/is-the-determinant-of-this-fibonacci-sum-indicator-matrix-always-1-0-or/513372",
      "locator": "derived from determinant parity equivalence"
    },
    "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": "derived from determinant parity equivalence"
  },
  "relations": [
    {
      "slug": "R298",
      "title": "Determinant equals a signed matching imbalance",
      "object_type": "claim",
      "relation": "addresses",
      "direction": "outgoing"
    },
    {
      "slug": "R299",
      "title": "Determinant equals a signed matching imbalance",
      "object_type": "claim",
      "relation": "addresses",
      "direction": "outgoing"
    }
  ]
}