{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R687",
  "content_hash": null,
  "slug": "rsh-claim-signed-binary-distinction",
  "type": "claim",
  "title": "Published binary formulas do not settle the signed determinant",
  "summary": "Han's periodic formula concerns the 0/1 Rudin-Shapiro sequence, while the candidate uses signs in \\(\\{-1,1\\}\\).",
  "relevance": "For Nonvanishing of Rudin-Shapiro Hankel determinants, record rsh-claim-signed-binary-distinction (“Published binary formulas do not settle the signed determinant”) records a bound, answer, status fact, or structural consequence. The record states: Han's periodic formula concerns the 0/1 Rudin-Shapiro sequence, while the candidate uses signs in \\(\\{-1,1\\}\\).",
  "relevance_source": "recorded",
  "body": "Han's Proposition 1.3 computes Hankel determinants modulo 2 for the binary sequence \\(u_n=(1-r_n)/2\\). Adamczewski and Rivoal construct selected Padé approximants for the signed generating function. Neither cited result states eventual nonvanishing of the leading signed Hankel minors. The signed and binary questions need separate records because reducing entries modulo 2 turns the signed Hankel matrix into an all-ones matrix.",
  "status": "established",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "universal",
    "statement": "the literature comparison for the signed sequence in the candidate"
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://doi.org/10.1016/j.aim.2016.08.013",
      "locator": "Han 2016, Proposition 1.3, pages 2-3; Adamczewski-Rivoal 2009, section 2.2 and Proposition 2.2"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1016/j.aim.2016.08.013",
    "locator": "Han 2016, Proposition 1.3, pages 2-3; Adamczewski-Rivoal 2009, section 2.2 and Proposition 2.2"
  },
  "models": [],
  "relations": [
    {
      "slug": "R688",
      "title": "Two residue classes are settled 2-adically",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "rudin-shapiro-hankel-nonvanishing",
      "title": "rudin shapiro hankel nonvanishing",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}