{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R680",
  "content_hash": null,
  "slug": "rsg-attempt-literature-audit",
  "type": "attempt",
  "title": "The literature gives ordinary squarefree-gap data, while the rainbow restriction remains unlocated",
  "summary": "Published searches certify the surrounding ordinary gaps, but the distinct square-prime matching variant did not appear in the sources reviewed.",
  "relevance": "For Largest rainbow squarefree gap below 10^12, record rsg-attempt-literature-audit (“The literature gives ordinary squarefree-gap data, while the rainbow restriction remains unlocated”) documents a concrete method, search boundary, or failed route. The record states: Published searches certify the surrounding ordinary gaps, but the distinct square-prime matching variant did not appear in the sources reviewed.",
  "relevance_source": "recorded",
  "body": "Marmet gives an Eratosthenes-style algorithm for first occurrences of runs of nonsquarefree integers and reports the first runs through length 18. Mossinghoff, Oliveira e Silva, and Trudgian independently study the empirical distribution of squarefree gaps through \\(10^{18}\\). Kumchev, McCormick, McNew, Park, Scherr, and Ziehr cite those computations when proving explicit universal gap bounds.\n\nFocused searches combined `squarefree gap`, `consecutive nonsquarefree`, `distinct prime squares`, `system of distinct representatives`, `Hall matching`, and `rainbow` with the cited authors and sequence data. The sources found treat ordinary gap length or its distribution. None imposes a different square-prime divisor at each interior position. This audit supports the upper bound and leaves novelty of the matching restriction unverified.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://arxiv.org/abs/1210.3829",
      "locator": "Louis Marmet, First occurrences of square-free gaps and an algorithm for their computation (2012); Michael J. Mossinghoff, Tomas Oliveira e Silva, and Timothy S. Trudgian, The distribution of k-free numbers, Mathematics of Computation 90 (2021), 907-929"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/1210.3829",
    "locator": "Louis Marmet, First occurrences of square-free gaps and an algorithm for their computation (2012); Michael J. Mossinghoff, Tomas Oliveira e Silva, and Timothy S. Trudgian, The distribution of k-free numbers, Mathematics of Computation 90 (2021), 907-929"
  },
  "models": [],
  "relations": [
    {
      "slug": "R681",
      "title": "Published squarefree-gap computations give the global upper bound 14",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "rainbow-squarefree-gap-1e12",
      "title": "rainbow squarefree gap 1e12",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}