{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1587",
  "content_hash": null,
  "slug": "hadamard-matrix-conjecture-status-packet-quality-20260801",
  "type": "claim",
  "title": "Dated status and exact unresolved remainder",
  "summary": "Unresolved in this packet after the dated source check. Strongest checked result: Cati and Pasechnik provide reproducible constructions through order 1208 for all known cases in that range and current tables beyond it. Their database improves many entries but continues to state the universal order-4k assertion as a conjecture. Exact unresolved remainder: Construct a Hadamard matrix of order 4k for every positive integer k, or give a positive k and prove that no matrix of order 4k exists.",
  "relevance": "For Hadamard matrix conjecture, this successor gives readable dated status prose and the exact remaining research boundary.",
  "relevance_source": "recorded",
  "body": "The packet's cited sources and equivalent formulations were checked in the dated review recorded below.\n\nStrongest checked result: Cati and Pasechnik provide reproducible constructions through order 1208 for all known cases in that range and current tables beyond it. Their database improves many entries but continues to state the universal order-4k assertion as a conjecture.\n\nExact unresolved remainder: Construct a Hadamard matrix of order 4k for every positive integer k, or give a positive k and prove that no matrix of order 4k exists.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://arxiv.org/abs/2402.13202",
      "locator": "abstract and section 1.1"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/2402.13202",
    "locator": "abstract and section 1.1"
  },
  "relations": [
    {
      "slug": "R1072",
      "title": "Current status and unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "outgoing"
    },
    {
      "slug": "hadamard-matrix-conjecture",
      "title": "hadamard matrix conjecture",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}