{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R862",
  "content_hash": null,
  "slug": "fib-formalization-total-unimodularity",
  "type": "formalization",
  "title": "Total unimodularity of the Fibonacci-sum matrix",
  "summary": "The checked Lean reduction combines Camion's criterion with the Fibonacci-specific divisibility obligation.",
  "relevance": "This strengthens the target to total unimodularity and connects its two proof obligations.",
  "relevance_source": "recorded",
  "body": "The checked declaration combines the verified Camion reduction with the Fibonacci support divisibility theorem. Every source dependency now compiles in the pinned world.",
  "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/TotalUnimodularity.lean"
    },
    "missing": [
      "source",
      "command",
      "expected_output"
    ]
  },
  "formal_statement": "theorem fibSumMatrix_totallyUnimodular (n : ℕ) : (fibSumMatrix n).IsTotallyUnimodular := by\n  classical\n  apply TheoremDB.Matrix.isTotallyUnimodular_of_camion\n  · intro i j\n    by_cases h : IsFibonacci (i.val + j.val + 2)\n    · use 1\n      simp [fibSumMatrix, h]\n    · use 0\n      simp [fibSumMatrix, h]\n  · exact fibSumMatrix_camion_divisibility n",
  "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/TotalUnimodularity.lean"
  },
  "relations": [
    {
      "slug": "R911",
      "title": "Lean determinant-range reduction",
      "object_type": "formalization",
      "relation": "depends_on",
      "direction": "incoming"
    },
    {
      "slug": "R904",
      "title": "Lean definition of the Fibonacci-sum matrix",
      "object_type": "formalization",
      "relation": "depends_on",
      "direction": "outgoing"
    },
    {
      "slug": "R860",
      "title": "Camion's total-unimodularity criterion",
      "object_type": "formalization",
      "relation": "depends_on",
      "direction": "outgoing"
    },
    {
      "slug": "R861",
      "title": "Fibonacci support divisibility condition",
      "object_type": "formalization",
      "relation": "depends_on",
      "direction": "outgoing"
    }
  ]
}