{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R654",
  "content_hash": null,
  "slug": "rls12-claim-published-estimate",
  "type": "claim",
  "title": "The primary order-12 estimate is 1.62 times 10^44",
  "summary": "McKay and Rogoyski estimated R_12 at 1.62e44 using an unbiased sequential-extension estimator over 1.1 million trials.",
  "relevance": "For Number of reduced Latin squares of order 12, record rls12-claim-published-estimate (“The primary order-12 estimate is 1.62 times 10^44”) records a bound, answer, status fact, or structural consequence. The record states: McKay and Rogoyski estimated R_12 at 1.62e44 using an unbiased sequential-extension estimator over 1.1 million trials.",
  "relevance_source": "recorded",
  "body": "McKay and Rogoyski generated a normalized Latin square row by row. At each step they chose uniformly among legal extensions with the required first-column entry. If \\(e_i\\) is the number of legal choices at step \\(i\\), then \\(e_1e_2\\cdots e_{n-1}\\) is an unbiased estimator of \\(R_n\\). Their Table 2 reports 1,100,000 trials for \\(n=12\\) and the estimate\n\\[\nR_{12}\\mathrel{\\approx}1.62\\times10^{44}.\n\\]\nThe authors described the displayed digits as probably accurate to one unit in the last shown digit. This value is statistical evidence. It is neither an exact integer nor a rigorous confidence interval.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "the 1,100,000 randomized trials reported for reduced Latin squares of order 12",
    "bounds": {
      "order": {
        "min": 12,
        "max": 12
      },
      "trials": {
        "min": 1100000,
        "max": 1100000
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://doi.org/10.37236/1222",
      "locator": "Brendan D. McKay and Eric Rogoyski, Latin Squares of Order 10, Electronic Journal of Combinatorics 2 (1995), #N3, Section 3 and Table 2"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.37236/1222",
    "locator": "Brendan D. McKay and Eric Rogoyski, Latin Squares of Order 10, Electronic Journal of Combinatorics 2 (1995), #N3, Section 3 and Table 2"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R652",
      "title": "The exact enumeration record ends at order 11",
      "object_type": "claim",
      "relation": "contextualizes",
      "direction": "outgoing"
    },
    {
      "slug": "reduced-latin-squares-order-12",
      "title": "reduced latin squares order 12",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}