{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R99",
  "content_hash": null,
  "slug": "ca32-claim-mdraco-near-solution",
  "type": "claim",
  "title": "The published heuristic search reached 17 violations",
  "summary": "After more than 10,000 CPU-days, mDRACO reported an order-32 permutation with 17 Costas-property violations.",
  "relevance": "For Existence of a Costas array of order 32, record ca32-claim-mdraco-near-solution (“The published heuristic search reached 17 violations”) records a bound, answer, status fact, or structural consequence. The record states: After more than 10,000 CPU-days, mDRACO reported an order-32 permutation with 17 Costas-property violations.",
  "relevance_source": "recorded",
  "body": "Vulakh and Finkel applied their parallel ant-colony solver to order 32 for more than 10,000 CPU-days. The best permutation reported in the paper has 17 Costas-property violations. The Appendix also lists near solutions with 18 and 19 violations.\n\nThis is useful search evidence because it gives a reproducible objective value and an explicit near solution in the primary source. The run was heuristic and did not cover the full permutation space. Seventeen repeated-vector violations therefore supplies neither a witness nor a lower bound on the minimum possible number of violations.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "the reported mDRACO search for an order-32 Costas permutation",
    "bounds": {
      "order": {
        "min": 32,
        "max": 32
      },
      "reported_cpu_days": {
        "min": 10000,
        "max": 10000
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://doi.org/10.1007/s00500-022-06969-1",
      "locator": "Vulakh and Finkel 2022, Section 4, page 5771, and Appendix: Arrays discovered"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1007/s00500-022-06969-1",
    "locator": "Vulakh and Finkel 2022, Section 4, page 5771, and Appendix: Arrays discovered"
  },
  "relations": [
    {
      "slug": "R98",
      "title": "Existence at order 32 remains open",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "costas-array-order-32",
      "title": "costas array order 32",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}