{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R75",
  "content_hash": null,
  "slug": "bsh-attempt-integer-nonvanishing",
  "type": "attempt",
  "title": "Find an integer recurrence or a vanishing counterexample",
  "summary": "The next search starts at order 5,000, while a proof must control even nonzero determinants as well as odd ones.",
  "relevance": "For Nonvanishing of Baum-Sweet Hankel determinants, record bsh-attempt-integer-nonvanishing (“Find an integer recurrence or a vanishing counterexample”) documents a concrete method, search boundary, or failed route. The record states: The next search starts at order 5,000, while a proof must control even nonzero determinants as well as odd ones.",
  "relevance_source": "recorded",
  "body": "Finite-field parity formulas cannot prove this claim because many of the integer determinants are even. A useful route would derive a recurrence for the integer leading minors from the 2-kernel of the sequence. A counterexample search should retain code and begin at \\(n=5000\\).",
  "status": "open_strategy",
  "evidence_grade": "proposed",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.1016/0022-314X(86)90083-1",
      "locator": "Mills and Robbins, Continued fractions for certain algebraic power series, Journal of Number Theory 23 (1986), pages 388-404"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1016/0022-314X(86)90083-1",
    "locator": "Mills and Robbins, Continued fractions for certain algebraic power series, Journal of Number Theory 23 (1986), pages 388-404"
  },
  "relations": [
    {
      "slug": "R74",
      "title": "One-prime modular audit through order 4,999",
      "object_type": "artifact",
      "relation": "uses",
      "direction": "outgoing"
    },
    {
      "slug": "baum-sweet-hankel-nonvanishing",
      "title": "baum sweet hankel nonvanishing",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}