{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R678",
  "content_hash": null,
  "slug": "rsbm10-claim-published-sequence-through-nine",
  "type": "claim",
  "title": "The current exact table ends at order nine",
  "summary": "OEIS A046747 lists the exact counts through S_9=902,616,230,040,448,613,437,952 and has no tenth term.",
  "relevance": "For Number of singular ten by ten binary matrices over the reals, record rsbm10-claim-published-sequence-through-nine (“The current exact table ends at order nine”) records a bound, answer, status fact, or structural consequence. The record states: OEIS A046747 lists the exact counts through S_9=902,616,230,040,448,613,437,952 and has no tenth term.",
  "relevance_source": "recorded",
  "body": "The current A046747 table gives\n\\[\n(S_1,\\ldots,S_9)=(1,10,338,42976,21040112,39882864736,\n292604283435872,8286284310367538176,902616230040448613437952).\n\\]\nIts July 2026 extension credits Dominik Beck for the order-nine term. The table contains no value for order ten as checked on 2026-07-25.\n\nŽivković's published classification partitions all binary matrices through order eight under row and column permutations. It gives 10,160,459,763,342,013,440 nonsingular matrices at order eight, whose complement in 2^64 is S_8 above. The order-nine figure is newer than that classification, and the audit located no primary paper or replayable orbit certificate for it. The order-nine value is therefore recorded as sourced database evidence.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "the published and database-listed exact counts of labeled real-singular binary square matrices for orders one through nine",
    "bounds": {
      "order": {
        "min": 1,
        "max": 9
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://oeis.org/A046747",
      "locator": "OEIS A046747, sequence and extensions sections checked 2026-07-25; Živković, Linear Algebra and its Applications 414 (2006), 310-346, DOI 10.1016/j.laa.2005.10.010"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://oeis.org/A046747",
    "locator": "OEIS A046747, sequence and extensions sections checked 2026-07-25; Živković, Linear Algebra and its Applications 414 (2006), 310-346, DOI 10.1016/j.laa.2005.10.010"
  },
  "models": [],
  "relations": [
    {
      "slug": "R677",
      "title": "The singular count is between 126,174,821,830,345,268,667,240,568,576 and 901,210,462,928,281,273,073,900,978,176",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "R674",
      "title": "Bareiss regression and exact order-ten bound verifier",
      "object_type": "artifact",
      "relation": "tests",
      "direction": "incoming"
    },
    {
      "slug": "real-singular-binary-matrices-ten",
      "title": "real singular binary matrices ten",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}