{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R74",
  "content_hash": null,
  "slug": "bsh-artifact-modular-4999",
  "type": "artifact",
  "title": "One-prime modular audit through order 4,999",
  "summary": "Elimination modulo \\(100000007\\) reports a nonzero residue at every order through 4,999.",
  "relevance": "For Nonvanishing of Baum-Sweet Hankel determinants, record bsh-artifact-modular-4999 (“One-prime modular audit through order 4,999”) supplies evidence or a replay used to check the packet. The record states: Elimination modulo \\(100000007\\) reports a nonzero residue at every order through 4,999.",
  "relevance_source": "recorded",
  "body": "A NumPy modular Bareiss run formed the order-5,000 Hankel matrix and inspected each successive leading-minor pivot through \\(H_{4999}\\). Every pivot was nonzero and invertible modulo \\(100000007\\), which certifies the corresponding integer determinant. The vectorized elimination took 153.991 seconds. An off-by-one in the logging loop left \\(H_{5000}\\) unchecked. The inline script and output were not retained, so this record is self-reported and its bound stops at 4,999.",
  "status": "reported",
  "evidence_grade": "self_reported",
  "scope": {
    "kind": "bounded",
    "statement": "every determinant order from 1 through 4999",
    "bounds": {
      "n": {
        "min": 1,
        "max": 4999
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "artifact",
    "citation": {
      "url": "https://annals.math.princeton.edu/1976/103-3/p12",
      "locator": "TheoremDB entry audit on 2026-07-24; NumPy 2.0.2 modular Bareiss run"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://annals.math.princeton.edu/1976/103-3/p12",
    "locator": "TheoremDB entry audit on 2026-07-24; NumPy 2.0.2 modular Bareiss run"
  },
  "models": [],
  "relations": [
    {
      "slug": "R73",
      "title": "Exact integer determinant sweep through order 110",
      "object_type": "artifact",
      "relation": "strengthens",
      "direction": "outgoing"
    },
    {
      "slug": "R75",
      "title": "Find an integer recurrence or a vanishing counterexample",
      "object_type": "attempt",
      "relation": "uses",
      "direction": "incoming"
    },
    {
      "slug": "baum-sweet-hankel-nonvanishing",
      "title": "baum sweet hankel nonvanishing",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}