{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R97",
  "content_hash": null,
  "slug": "ca32-attempt-construction-record-audit",
  "type": "attempt",
  "title": "Standard construction and record audit",
  "summary": "The principal Welch and Golomb parameter routes miss order 32, and the current known-array records contain no order-32 witness.",
  "relevance": "For Existence of a Costas array of order 32, record ca32-attempt-construction-record-audit (“Standard construction and record audit”) documents a concrete method, search boundary, or failed route. The record states: The principal Welch and Golomb parameter routes miss order 32, and the current known-array records contain no order-32 witness.",
  "relevance_source": "recorded",
  "body": "The principal Welch \\(W_1\\) construction has order \\(p-1\\) for a prime \\(p\\). At order 32 it would require \\(p=33\\), which is composite. The principal Golomb \\(G_2\\) construction has order \\(q-2\\) for a prime power \\(q\\). At order 32 it would require \\(q=34\\), which is not a prime power. These arithmetic checks explain why the two main infinite families do not immediately settle this order.\n\nPublished construction tables list no successful construction at 32. Beard's archive includes generated arrays at many larger orders and searched arrays through order 29, yet gives no order-32 permutation. Gulec and Abolghasemi's 2026 study uses the same known-array record and still describes complete enumeration only through order 29.\n\nThis audit covers known records and the two principal algebraic families. It does not exclude a sporadic array, an unrecorded computation, or a new construction.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "standard algebraic construction parameters and published records bearing on order 32",
    "bounds": {
      "order": {
        "min": 32,
        "max": 32
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.1145/1916461.1916465",
      "locator": "Taylor, Rickard, and Drakakis, Costas arrays: Survey, standardization, and MATLAB toolbox, ACM Transactions on Mathematical Software 37(4) (2011), construction definitions and tables; Beard database index; Gulec and Abolghasemi 2026, Introduction"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1145/1916461.1916465",
    "locator": "Taylor, Rickard, and Drakakis, Costas arrays: Survey, standardization, and MATLAB toolbox, ACM Transactions on Mathematical Software 37(4) (2011), construction definitions and tables; Beard database index; Gulec and Abolghasemi 2026, Introduction"
  },
  "relations": [
    {
      "slug": "R98",
      "title": "Existence at order 32 remains open",
      "object_type": "claim",
      "relation": "supports",
      "direction": "outgoing"
    },
    {
      "slug": "costas-array-order-32",
      "title": "costas array order 32",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}