{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R298",
  "content_hash": null,
  "slug": "fib-claim-parity-equivalence",
  "type": "claim",
  "title": "Determinant equals a signed matching imbalance",
  "summary": "The determinant conjecture is equivalent to saying that allowed even and odd permutations differ in count by at most one.",
  "relevance": "For fib problem determinant range; fib problem nonzero support, record fib-claim-parity-equivalence (“Determinant equals a signed matching imbalance”) records a bound, answer, status fact, or structural consequence. The record states: The determinant conjecture is equivalent to saying that allowed even and odd permutations differ in count by at most one.",
  "relevance_source": "recorded",
  "body": "Allowed permutations satisfy that i+pi(i) is Fibonacci for every row i.",
  "status": "established",
  "evidence_grade": "mathematical_identity",
  "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": "question line 60"
    },
    "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": "question line 60"
  },
  "relations": [
    {
      "slug": "fib-problem-determinant-range",
      "title": "Fibonacci-sum indicator determinant conjecture",
      "object_type": "problem",
      "relation": "reformulates",
      "direction": "outgoing"
    },
    {
      "slug": "R287",
      "title": "Cancellation at n=33 is exact",
      "object_type": "claim",
      "relation": "supports",
      "direction": "incoming"
    },
    {
      "slug": "R275",
      "title": "Construct a sign-reversing involution on allowed permutations",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "R276",
      "title": "Use the signed perfect-matching graph",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "R299",
      "title": "Determinant equals a signed matching imbalance",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "incoming"
    }
  ]
}