{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R652",
  "content_hash": null,
  "slug": "rls12-claim-current-status",
  "type": "claim",
  "title": "The exact enumeration record ends at order 11",
  "summary": "The exact value of R_12 remains open. The last published exact count is R_11, while the published order-12 figure is a randomized estimate.",
  "relevance": "For Number of reduced Latin squares of order 12, record rls12-claim-current-status (“The exact enumeration record ends at order 11”) records a bound, answer, status fact, or structural consequence. The record states: The exact value of R_12 remains open.",
  "relevance_source": "recorded",
  "body": "McKay and Wanless completed the exact enumeration through order 11. Their paper gives \\(R_{11}=5363937773277371298119673540771840\\) and says that the same graph-classification method was unlikely to reach \\(R_{12}\\) soon because there are more than \\(10^{11}\\) regular bipartite graphs of order 24 and degree 6.\n\nMcKay and Rogoyski had earlier reported a randomized estimate for order 12. Stones's 2010 survey explicitly says that \\(R_{12}\\) is unknown and lists the exact sequence only through order 11. A search on 2026-07-25 of the exact-count papers, the later order-11 class enumeration, the survey literature, and the current author-maintained count table found no subsequent exact value. The candidate therefore remains an open exact-enumeration problem.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "the published exact enumeration record for reduced Latin squares through order 12, audited on 2026-07-25",
    "bounds": {
      "order": {
        "min": 1,
        "max": 12
      }
    },
    "exhaustive": false
  },
  "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, Annals of Combinatorics 9 (2005), 335-344, Section 3 and Table 1; Douglas S. Stones, The Many Formulae for the Number of Latin Rectangles, Electronic Journal of Combinatorics 17 (2010), #A1, Figure 1"
    },
    "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, Annals of Combinatorics 9 (2005), 335-344, Section 3 and Table 1; Douglas S. Stones, The Many Formulae for the Number of Latin Rectangles, Electronic Journal of Combinatorics 17 (2010), #A1, Figure 1"
  },
  "models": [],
  "relations": [
    {
      "slug": "R654",
      "title": "The primary order-12 estimate is 1.62 times 10^44",
      "object_type": "claim",
      "relation": "contextualizes",
      "direction": "incoming"
    },
    {
      "slug": "R655",
      "title": "A rigorous elementary bracket contains the estimate",
      "object_type": "claim",
      "relation": "bounds",
      "direction": "incoming"
    },
    {
      "slug": "reduced-latin-squares-order-12",
      "title": "reduced latin squares order 12",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}