{
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  "ref": "R1697",
  "content_hash": null,
  "slug": "pi-not-badly-approximable-status-packet-quality-20260801",
  "type": "claim",
  "title": "Dated status and exact unresolved remainder",
  "summary": "Unresolved in this packet after the dated source check. Strongest checked result: The MathOverflow answer identifies the question with the open problem of proving unbounded partial quotients for \\(\\pi\\). Current explicit upper bounds for the irrationality measure of \\(\\pi\\) do not establish this target. Exact unresolved remainder: 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": "For Unbounded continued-fraction coefficients of pi, this successor gives readable dated status prose and the exact remaining research boundary.",
  "relevance_source": "recorded",
  "body": "The packet's cited sources and equivalent formulations were checked in the dated review recorded below.\n\nStrongest checked result: The MathOverflow answer identifies the question with the open problem of proving unbounded partial quotients for \\(\\pi\\). Current explicit upper bounds for the irrationality measure of \\(\\pi\\) do not establish this target.\n\nExact unresolved remainder: 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.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://arxiv.org/abs/1912.06345",
      "locator": "abstract and main theorem proving mu(pi) <= 7.103205334137..."
    },
    "missing": [
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  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/1912.06345",
    "locator": "abstract and main theorem proving mu(pi) <= 7.103205334137..."
  },
  "relations": [
    {
      "slug": "R1352",
      "title": "Current checked status and unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "outgoing"
    },
    {
      "slug": "pi-not-badly-approximable",
      "title": "pi not badly approximable",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
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}