{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R278",
  "content_hash": null,
  "slug": "fib-attempt-singleton-peeling-scoped",
  "type": "attempt",
  "title": "Reduce by forced singleton rows and columns",
  "summary": "Repeatedly expand along a row or column with one nonzero entry and hope the matrix disappears.",
  "relevance": "For fib problem determinant range; fib problem nonzero support, record fib-attempt-singleton-peeling-scoped (“Reduce by forced singleton rows and columns”) documents a concrete method, search boundary, or failed route. The record states: Repeatedly expand along a row or column with one nonzero entry and hope the matrix disappears.",
  "relevance_source": "recorded",
  "body": "The method leaves a residual core in 110 of the first 120 cases, so it supplies a reduction rather than a complete proof.",
  "status": "failed_as_complete_proof",
  "evidence_grade": "reproduced",
  "scope": {
    "kind": "bounded",
    "statement": "tested against every size from 1 to 120",
    "bounds": {
      "n": {
        "min": 1,
        "max": 120
      }
    },
    "exhaustive": true
  },
  "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": "theoremdb frontier pilot and research/fibonacci/checks.py"
    },
    "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": "theoremdb frontier pilot and research/fibonacci/checks.py"
  },
  "models": [],
  "relations": [
    {
      "slug": "R304",
      "title": "Singleton peeling usually leaves a residual core",
      "object_type": "claim",
      "relation": "refutes_as_complete_method",
      "direction": "incoming"
    },
    {
      "slug": "R289",
      "title": "Forced peeling reduces the determinant to a core determinant",
      "object_type": "claim",
      "relation": "salvages",
      "direction": "incoming"
    },
    {
      "slug": "fib-problem-determinant-range",
      "title": "Fibonacci-sum indicator determinant conjecture",
      "object_type": "problem",
      "relation": "addresses",
      "direction": "outgoing"
    },
    {
      "slug": "R277",
      "title": "Reduce by forced singleton rows and columns",
      "object_type": "attempt",
      "relation": "supersedes",
      "direction": "outgoing",
      "metadata": {
        "reason": "This revision records the reviewed scope explicitly."
      }
    }
  ]
}