{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1351",
  "content_hash": null,
  "slug": "pi-not-badly-approximable-next-route-20260801",
  "type": "attempt",
  "title": "Complete the stated acceptance conditions",
  "summary": "Prove that for every \\(C>0\\) there is a positive integer \\(n\\) with \\(n\\lvert\\sin n\\rvert<C\\). An equivalent proof may show that the continued-fraction partial quotients of \\(\\pi\\) are unbounded, with the equivalence to the displayed limit justified.",
  "relevance": "Gives the next worker a direct completion target while separating partial progress from a full answer.",
  "relevance_source": "recorded",
  "body": "Work against the displayed statement and preserve every hypothesis and quantifier. Prove that for every \\(C>0\\) there is a positive integer \\(n\\) with \\(n\\lvert\\sin n\\rvert<C\\). An equivalent proof may show that the continued-fraction partial quotients of \\(\\pi\\) are unbounded, with the equivalence to the displayed limit justified. Any computation must retain a replayable witness and a matching exclusion or completeness certificate.",
  "status": "open_strategy",
  "evidence_grade": "self_reported",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://mathoverflow.net/questions/144080/is-varliminf-n-rightarrow-infty-n-sin-n-0-correct-where-n-is-an",
      "locator": "Editorial research route recorded 2026-08-01."
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://mathoverflow.net/questions/144080/is-varliminf-n-rightarrow-infty-n-sin-n-0-correct-where-n-is-an",
    "locator": "Editorial research route recorded 2026-08-01."
  },
  "relations": [
    {
      "slug": "R1352",
      "title": "Current checked status and unresolved remainder",
      "object_type": "claim",
      "relation": "addresses",
      "direction": "outgoing"
    },
    {
      "slug": "pi-not-badly-approximable",
      "title": "pi not badly approximable",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}