{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R686",
  "content_hash": null,
  "slug": "rsh-attempt-residue-class-two",
  "type": "attempt",
  "title": "Settle the remaining orders congruent to 2 modulo 3",
  "summary": "The open core is \\(H_{3m+2}\\neq0\\) for every \\(m\\geq3\\).",
  "relevance": "For Nonvanishing of Rudin-Shapiro Hankel determinants, record rsh-attempt-residue-class-two (“Settle the remaining orders congruent to 2 modulo 3”) documents a concrete method, search boundary, or failed route. The record states: The open core is \\(H_{3m+2}\\neq0\\) for every \\(m\\geq3\\).",
  "relevance_source": "recorded",
  "body": "The 2-adic argument becomes inconclusive in this residue class because the reduced determinant is even. A useful next step is a continued-fraction or modular recurrence that treats \\(H_{3m+2}\\) directly. Any counterexample search should begin above the certified bound 5,000.",
  "status": "open_strategy",
  "evidence_grade": "proposed",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://arxiv.org/abs/1711.10764",
      "locator": "Mérai and Winterhof, On the Nth linear complexity of automatic sequences, Theorem 2"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/1711.10764",
    "locator": "Mérai and Winterhof, On the Nth linear complexity of automatic sequences, Theorem 2"
  },
  "relations": [
    {
      "slug": "R688",
      "title": "Two residue classes are settled 2-adically",
      "object_type": "claim",
      "relation": "uses",
      "direction": "outgoing"
    },
    {
      "slug": "R685",
      "title": "Modular nonvanishing certificates through order 5,000",
      "object_type": "artifact",
      "relation": "uses",
      "direction": "outgoing"
    },
    {
      "slug": "rudin-shapiro-hankel-nonvanishing",
      "title": "rudin shapiro hankel nonvanishing",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}