{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R198",
  "content_hash": null,
  "slug": "dclp-attempt-literature-audit",
  "type": "attempt",
  "title": "The literature establishes enumeration and precise asymptotics",
  "summary": "The focused audit found the sequence, its limit, and full asymptotics, with no theorem giving the requested threshold.",
  "relevance": "For Eventual decrease for distinct cycle lengths in random permutations, record dclp-attempt-literature-audit (“The literature establishes enumeration and precise asymptotics”) documents a concrete method, search boundary, or failed route. The record states: The focused audit found the sequence, its limit, and full asymptotics, with no theorem giving the requested threshold.",
  "relevance_source": "recorded",
  "body": "Lehmer studies the same reciprocal weights on distinct partitions and proves the limit \\(e^{-\\gamma}\\). Greene and Knuth obtain the first useful error term. Flajolet and coauthors derive the full root-of-unity expansion. Knopfmacher and Warlimont place the product in a broader class of restricted cycle types.\n\nSearches using the sequence number, the product, `permutations with distinct cycle lengths`, `monotonicity`, and `decreasing probability` located no primary source proving strict decrease after 30. This audit supports an unresolved status rather than a claim that the question is new.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.4064/aa-21-1-379-388",
      "locator": "D. H. Lehmer, Acta Arithmetica 21 (1972), 379-388; Flajolet et al., EJC 13 (2006), R103; A. Knopfmacher and R. Warlimont, Australasian Journal of Combinatorics 13 (1996), 151-162"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.4064/aa-21-1-379-388",
    "locator": "D. H. Lehmer, Acta Arithmetica 21 (1972), 379-388; Flajolet et al., EJC 13 (2006), R103; A. Knopfmacher and R. Warlimont, Australasian Journal of Combinatorics 13 (1996), 151-162"
  },
  "models": [],
  "relations": [
    {
      "slug": "dclp-problem-eventual-strict-decrease",
      "title": "Does the distinct-cycle-length probability decrease after n=30?",
      "object_type": "problem",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "distinct-cycle-length-probability-decreasing",
      "title": "distinct cycle length probability decreasing",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}