{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R861",
  "content_hash": null,
  "slug": "fib-formalization-camion-divisibility",
  "type": "formalization",
  "title": "Fibonacci support divisibility condition",
  "summary": "The problem-specific Lean obligation says that every square Fibonacci-sum submatrix with even row and column sums contains a multiple of four ones.",
  "relevance": "This checked bridge connects the graph-theoretic support theorem to Camion's integer matrix condition.",
  "relevance_source": "recorded",
  "body": "The kernel-checked proof converts the matrix-entry sum to the finite support cardinality and applies the checked odd-square-cover theorem.",
  "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/Divisibility.lean"
    },
    "missing": [
      "source",
      "command",
      "expected_output"
    ]
  },
  "formal_statement": "theorem fibSumMatrix_camion_divisibility (n k : ℕ) (f : Fin k → Fin n) (g : Fin k → Fin n) (hf : f.Injective) (hg : g.Injective) (hrows : HasEvenRowSums ((fibSumMatrix n).submatrix f g)) (hcols : HasEvenColumnSums ((fibSumMatrix n).submatrix f g)) : (4 : ℤ) ∣ entrySum ((fibSumMatrix n).submatrix f g) := by\n  rw [entrySum_fibSumMatrix_submatrix]\n  exact_mod_cast fibSubmatrixSupport_card_dvd_four n k f g hf hg hrows hcols",
  "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/Divisibility.lean"
  },
  "relations": [
    {
      "slug": "R862",
      "title": "Total unimodularity of the Fibonacci-sum matrix",
      "object_type": "formalization",
      "relation": "depends_on",
      "direction": "incoming"
    },
    {
      "slug": "R863",
      "title": "Fibonacci odd square cover",
      "object_type": "formalization",
      "relation": "depends_on",
      "direction": "outgoing"
    }
  ]
}