{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R275",
  "content_hash": null,
  "slug": "fib-attempt-sign-involution",
  "type": "attempt",
  "title": "Construct a sign-reversing involution on allowed permutations",
  "summary": "Pair allowed permutations of opposite parity, leaving at most one fixed exception, to explain the determinant bound directly.",
  "relevance": "For fib problem determinant range; fib problem nonzero support, record fib-attempt-sign-involution (“Construct a sign-reversing involution on allowed permutations”) documents a concrete method, search boundary, or failed route. The record states: Pair allowed permutations of opposite parity, leaving at most one fixed exception, to explain the determinant bound directly.",
  "relevance_source": "recorded",
  "body": "The Fibonacci carry structure may identify the first local difference to switch. No valid involution has been constructed.",
  "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 the permutation 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 the permutation 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"
    }
  ]
}