{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R653",
  "content_hash": null,
  "slug": "rls12-claim-order-11-calibration",
  "type": "claim",
  "title": "The order-11 exact count fixes the normalization",
  "summary": "The published values satisfy L_11=11!10!R_11 exactly, separating reduced squares from all labelled squares.",
  "relevance": "For Number of reduced Latin squares of order 12, record rls12-claim-order-11-calibration (“The order-11 exact count fixes the normalization”) records a bound, answer, status fact, or structural consequence. The record states: The published values satisfy L_11=11!10!R_11 exactly, separating reduced squares from all labelled squares.",
  "relevance_source": "recorded",
  "body": "For order \\(n\\), every reduced Latin square has exactly \\(n!(n-1)!\\) labelled forms, so\n\\[\nL_n=n!(n-1)!R_n.\n\\]\nMcKay and Wanless give\n\\[\nR_{11}=5363937773277371298119673540771840\n\\]\nand\n\\[\nL_{11}=776966836171770144107444346734230682311065600000.\n\\]\nThe companion replay checks the multiplication exactly. This calibration prevents the common error of substituting a count of labelled squares, isotopy classes, or main classes for the reduced count requested by the candidate.",
  "status": "established",
  "evidence_grade": "reproduced",
  "scope": {
    "kind": "bounded",
    "statement": "all reduced and labelled Latin squares of order 11",
    "bounds": {
      "order": {
        "min": 11,
        "max": 11
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://doi.org/10.1007/s00026-005-0261-7",
      "locator": "McKay and Wanless, On the Number of Latin Squares, definition in Section 1 and R_11 in Table 1; independently checked in rls12-artifact-small-order-replay"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1007/s00026-005-0261-7",
    "locator": "McKay and Wanless, On the Number of Latin Squares, definition in Section 1 and R_11 in Table 1; independently checked in rls12-artifact-small-order-replay"
  },
  "models": [],
  "relations": [
    {
      "slug": "R651",
      "title": "Exact small-order enumeration and order-12 arithmetic replay",
      "object_type": "artifact",
      "relation": "reproduces",
      "direction": "incoming"
    },
    {
      "slug": "reduced-latin-squares-order-12",
      "title": "reduced latin squares order 12",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}