{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R684",
  "content_hash": null,
  "slug": "rsh-artifact-determinants-110",
  "type": "artifact",
  "title": "Exact signed determinant sweep through order 110",
  "summary": "Bareiss elimination finds zeros exactly at orders \\(2,5,8\\) through \\(n=110\\).",
  "relevance": "For Nonvanishing of Rudin-Shapiro Hankel determinants, record rsh-artifact-determinants-110 (“Exact signed determinant sweep through order 110”) supplies evidence or a replay used to check the packet. The record states: Bareiss elimination finds zeros exactly at orders \\(2,5,8\\) through \\(n=110\\).",
  "relevance_source": "recorded",
  "body": "The checker generates \\(r_n=(-1)^{\\operatorname{popcount}(n\\mathbin{\\&}(n\\!\\gg\\!1))}\\) and computes every leading Hankel determinant over the integers. The first twelve values are \\(1,0,-4,-8,0,32,-192,0,6912,10752,-112640,-780288\\). No zero occurs after order 8 in the checked range.",
  "status": "available",
  "evidence_grade": "executable",
  "scope": {
    "kind": "bounded",
    "statement": "every determinant order from 1 through 110",
    "bounds": {
      "n": {
        "min": 1,
        "max": 110
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "partial",
    "kind": "python_computation",
    "source": "research/candidate-screening/verify.py",
    "citation": {
      "url": "https://github.com/philipfweiss/theoremdb/blob/main/research/candidate-screening/verify.py",
      "locator": "research/candidate-screening/verify.py and verified_ranges.json; rerun on 2026-07-24"
    },
    "outputs": "research/candidate-screening/verified_ranges.json",
    "missing": [
      "command",
      "runtime"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://github.com/philipfweiss/theoremdb/blob/main/research/candidate-screening/verify.py",
    "locator": "research/candidate-screening/verify.py and verified_ranges.json; rerun on 2026-07-24"
  },
  "relations": [
    {
      "slug": "R688",
      "title": "Two residue classes are settled 2-adically",
      "object_type": "claim",
      "relation": "tests",
      "direction": "outgoing"
    },
    {
      "slug": "R685",
      "title": "Modular nonvanishing certificates through order 5,000",
      "object_type": "artifact",
      "relation": "strengthens",
      "direction": "incoming"
    },
    {
      "slug": "rudin-shapiro-hankel-nonvanishing",
      "title": "rudin shapiro hankel nonvanishing",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}