{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R904",
  "content_hash": null,
  "slug": "fib-formalization-matrix-lean-v1",
  "type": "formalization",
  "title": "Lean definition of the Fibonacci-sum matrix",
  "summary": "The checked Lean object uses Matrix (Fin n) (Fin n) Int with entries determined by Fibonacci membership after converting indices to one-based naturals.",
  "relevance": "For fib problem determinant range; fib problem nonzero support, record fib-formalization-matrix-lean-v1 (“Lean definition of the Fibonacci-sum matrix”) states a machine-checkable theorem or proof obligation. The record states: The checked Lean object uses Matrix (Fin n) (Fin n) Int with entries determined by Fibonacci membership after converting indices to one-based naturals.",
  "relevance_source": "recorded",
  "body": "This definition elaborates in the pinned TheoremDB world. It has not received a signed worker attestation.",
  "status": "draft",
  "evidence_grade": "unverified_formalization",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "partial",
    "kind": "formalization",
    "runtime": "lean-4.33.0-rc1/mathlib4@4608056c77c52468b80773e8dcd585ef821c7c5e+theoremdb@d575c4e2ff28345440c4f8a42bf0178bcb3f6f41b703a45d9d1cbb709036f0dc",
    "citation": {
      "url": "https://mathoverflow.net/questions/513340/is-the-determinant-of-this-fibonacci-sum-indicator-matrix-always-1-0-or/513372",
      "locator": "formal/lean/TheoremDB/Fibonacci/Basic.lean"
    },
    "missing": [
      "source",
      "command",
      "expected_output"
    ]
  },
  "formal_statement": "noncomputable def fibSumMatrix (n : ℕ) : Matrix (Fin n) (Fin n) ℤ := fun i j => if IsFibonacci (i.val + j.val + 2) then 1 else 0",
  "source": {
    "url": "https://mathoverflow.net/questions/513340/is-the-determinant-of-this-fibonacci-sum-indicator-matrix-always-1-0-or/513372",
    "locator": "formal/lean/TheoremDB/Fibonacci/Basic.lean"
  },
  "models": [],
  "relations": [
    {
      "slug": "fib-problem-determinant-range",
      "title": "Fibonacci-sum indicator determinant conjecture",
      "object_type": "problem",
      "relation": "formalizes",
      "direction": "outgoing"
    },
    {
      "slug": "R313",
      "title": "Draft Lean definition of the Fibonacci-sum matrix",
      "object_type": "formalization",
      "relation": "supersedes",
      "direction": "outgoing",
      "metadata": {
        "reason": "Replaces the design sketch with the checked pinned-world definition."
      }
    },
    {
      "slug": "R862",
      "title": "Total unimodularity of the Fibonacci-sum matrix",
      "object_type": "formalization",
      "relation": "depends_on",
      "direction": "incoming"
    },
    {
      "slug": "R865",
      "title": "Fibonacci support four-cycle classification",
      "object_type": "formalization",
      "relation": "depends_on",
      "direction": "incoming"
    }
  ]
}