{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R66",
  "content_hash": null,
  "slug": "bdr1m-attempt-literature-audit",
  "type": "attempt",
  "title": "The literature audit found asymptotic and central-coefficient results",
  "summary": "The sources located do not give the two-parameter bounded record at one million.",
  "relevance": "For Most divisors of a binomial coefficient with top at most 10^6, record bdr1m-attempt-literature-audit (“The literature audit found asymptotic and central-coefficient results”) documents a concrete method, search boundary, or failed route. The record states: The sources located do not give the two-parameter bounded record at one million.",
  "relevance_source": "recorded",
  "body": "OEIS A048784 tabulates \\(\\tau\\binom{2m}{m}\\) for central binomial coefficients and cites Fedorov's asymptotic formula for that sequence. Fedorov's separate Mathematical Notes paper studies upper and lower orders of ratios between divisor counts of adjacent binomial coefficients. Erdős and Kolesnik study prime-power divisibility near the middle. These sources concern central values, asymptotics, or individual prime powers.\n\nSearches by the exact objective, divisor-record terminology, and the pair of bounds \\(k<n\\leq10^6\\) found no published table or complete two-parameter sweep. The exact value at the requested cutoff therefore remains unresolved in this record. The prefix theorem and cutoff-scale lower bound above are the certified results supplied here.",
  "status": "inconclusive",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "universal",
    "statement": "published and public-sequence work on divisor counts and prime exponents of binomial coefficients"
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://oeis.org/A048784",
      "locator": "OEIS A048784; G. V. Fedorov, On the number of divisors of binomial coefficients, Mathematical Notes 93 (2013), 308-316, DOI 10.1134/S0001434613010331; Paul Erdős and Grigori Kolesnik, Prime power divisors of binomial coefficients, Discrete Mathematics 200 (1999), 101-117, DOI 10.1016/S0012-365X(98)00326-4"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://oeis.org/A048784",
    "locator": "OEIS A048784; G. V. Fedorov, On the number of divisors of binomial coefficients, Mathematical Notes 93 (2013), 308-316, DOI 10.1134/S0001434613010331; Paul Erdős and Grigori Kolesnik, Prime power divisors of binomial coefficients, Discrete Mathematics 200 (1999), 101-117, DOI 10.1016/S0012-365X(98)00326-4"
  },
  "relations": [
    {
      "slug": "R68",
      "title": "The exact record through n=20,000 occurs at (19,971, 9,949)",
      "object_type": "claim",
      "relation": "contextualizes",
      "direction": "outgoing"
    },
    {
      "slug": "binomial-divisor-record-1e6",
      "title": "binomial divisor record 1e6",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}