{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R593",
  "content_hash": null,
  "slug": "pp12-attempt-literature-and-catalogue-audit",
  "type": "attempt",
  "title": "Primary literature and small-plane catalogue audit",
  "summary": "The audit located strong arithmetic and symmetry restrictions, a five-MOLS construction, and exact reformulations, while the existence question stayed open.",
  "relevance": "For A projective plane of order 12, record pp12-attempt-literature-and-catalogue-audit (“Primary literature and small-plane catalogue audit”) documents a concrete method, search boundary, or failed route. The record states: The audit located strong arithmetic and symmetry restrictions, a five-MOLS construction, and exact reformulations, while the existence question stayed open.",
  "relevance_source": "recorded",
  "body": "The audit checked the 1949 Bruck-Ryser paper, the 1960 five-MOLS construction, the 2019 order-9 collineation exclusion, the 2023 order-4 exclusion, and the 2023 Hadamard equivalence. It also checked Eric Moorhouse's Projective Planes of Small Order catalogue, which describes itself as a current list of known small planes and includes every known plane below order 34 known to its maintainer. The table has no order-12 incidence record.\n\nThe catalogue states that its completeness guarantee ends at order 10. Its empty order-12 slot therefore serves as a database cross-check rather than a mathematical exclusion. The strongest global restriction found is the 2023 theorem that every collineation group has order 1, 2, or 3. The strongest explicit partial Latin-square object found remains a family of five MOLS. The complete family of 11 remains unconstructed.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://ericmoorhouse.org/pub/planes/",
      "locator": "Eric Moorhouse, Projective Planes of Small Order, catalogue description and order table, accessed 2026-07-25; primary sources listed in metadata"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://ericmoorhouse.org/pub/planes/",
    "locator": "Eric Moorhouse, Projective Planes of Small Order, catalogue description and order table, accessed 2026-07-25; primary sources listed in metadata"
  },
  "models": [],
  "relations": [
    {
      "slug": "R597",
      "title": "Existence at order 12 remains open",
      "object_type": "claim",
      "relation": "supports",
      "direction": "outgoing"
    },
    {
      "slug": "projective-plane-order-12",
      "title": "projective plane order 12",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}