{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R675",
  "content_hash": null,
  "slug": "rsbm10-attempt-literature-and-enumeration-audit",
  "type": "attempt",
  "title": "The exact order-ten count was not located",
  "summary": "Published classification reaches order eight, the current sequence reaches order nine, and probability papers give asymptotic results.",
  "relevance": "For Number of singular ten by ten binary matrices over the reals, record rsbm10-attempt-literature-and-enumeration-audit (“The exact order-ten count was not located”) documents a concrete method, search boundary, or failed route. The record states: Published classification reaches order eight, the current sequence reaches order nine, and probability papers give asymptotic results.",
  "relevance_source": "recorded",
  "body": "Metropolis and Stein counted a broad structural family of singular binary matrices using binomial coefficients and signed Stirling numbers. Živković classified row and column permutation classes through order eight. Bourgain, Vu, and Wood proved exponential singularity bounds for discrete random matrices. Tikhomirov later proved the sharp exponential scale for uniform sign matrices. These sources establish the finite counting framework and the asymptotic scale.\n\nThe targeted search found no primary source giving S_10. OEIS A046747 was updated in July 2026 with S_9 and still ends there. This table endpoint is evidence about the search, rather than proof of novelty.\n\nAn exact continuation should enumerate row and column permutation orbits of 10 by 10 bipartite adjacency matrices. For each canonical orbit representative, exact Bareiss elimination decides real singularity, while the reciprocal automorphism-group order supplies its labeled weight. The certificate should preserve every representative, its automorphism order, determinant or rank, and a running weighted checksum. Independent sums must recover 2^100 across all orbits and the stated singular total across the zero-determinant orbits.",
  "status": "inconclusive",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "a targeted audit of exact binary-matrix enumeration and random Bernoulli singularity sources for order ten, completed on 2026-07-25",
    "bounds": {
      "target_order": {
        "min": 10,
        "max": 10
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.1016/j.laa.2005.10.010",
      "locator": "Metropolis and Stein, J. Combinatorial Theory 3 (1967), 191-198, DOI 10.1016/S0021-9800(67)80006-1; Živković, Linear Algebra and its Applications 414 (2006), 310-346, DOI 10.1016/j.laa.2005.10.010; Bourgain, Vu, and Wood, J. Functional Analysis 258 (2010), 559-603, DOI 10.1016/j.jfa.2009.04.016; Tikhomirov, Annals of Mathematics 191 (2020), 593-634, DOI 10.4007/annals.2020.191.2.6"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1016/j.laa.2005.10.010",
    "locator": "Metropolis and Stein, J. Combinatorial Theory 3 (1967), 191-198, DOI 10.1016/S0021-9800(67)80006-1; Živković, Linear Algebra and its Applications 414 (2006), 310-346, DOI 10.1016/j.laa.2005.10.010; Bourgain, Vu, and Wood, J. Functional Analysis 258 (2010), 559-603, DOI 10.1016/j.jfa.2009.04.016; Tikhomirov, Annals of Mathematics 191 (2020), 593-634, DOI 10.4007/annals.2020.191.2.6"
  },
  "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": "real-singular-binary-matrices-ten",
      "title": "real singular binary matrices ten",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}