{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R453",
  "content_hash": null,
  "slug": "levine-attempt-replay-81-224-certificate",
  "type": "attempt",
  "title": "The published 81/224 matrix optimization has an independent exact replay",
  "summary": "A full set-partition enumeration now certifies the displayed hint matrix's value as \\(81/224\\) and matches the reported count of 3,920 maximizers.",
  "relevance": "For The value of Levine's two-player coin-index game, record levine-attempt-replay-81-224-certificate (“The published 81/224 matrix optimization has an independent exact replay”) documents a concrete method, search boundary, or failed route. The record states: A full set-partition enumeration now certifies the displayed hint matrix's value as \\(81/224\\) and matches the reported count of 3,920 maximizers.",
  "relevance_source": "recorded",
  "body": "The source audit found the balanced \\(8\\times14\\) matrix and the authors' result in the journal and arXiv source, with no original enumeration code. A first bounded artifact independently recovered and checked one attaining four-class partition.\n\nThe follow-up C++ replay enumerates all 190,899,322 unlabeled partitions of the fourteen columns. Within every partition it exhausts every binary coloring of the classes and performs exact integer row scoring. It obtains global maximum \\(81/224\\), with 2,016 attaining partitions having four classes, 560 having five, and 1,344 having six. Their total, 3,920, matches the paper. This supplies an independent executable certificate for the finite matrix optimization.\n\nBuhler and coauthors' matrix-hint theorem turns that finite maximum into the universal upper bound \\(p^*\\le81/224\\). The replay checks the finite premise of that theorem. It does not improve the endpoint or settle whether \\(p^*=7/20\\).",
  "status": "completed",
  "evidence_grade": "computational",
  "scope": {
    "kind": "bounded",
    "statement": "the published balanced hint matrix used for the 81/224 upper bound",
    "bounds": {
      "hint_matrix_rows": {
        "min": 8,
        "max": 8
      },
      "hint_matrix_columns": {
        "min": 14,
        "max": 14
      },
      "reported_attaining_partitions": {
        "min": 3920,
        "max": 3920
      },
      "partitions_checked": {
        "min": 190899322,
        "max": 190899322
      },
      "partition_colorings_checked": {
        "min": 20732504062,
        "max": 20732504062
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://arxiv.org/abs/1407.4711",
      "locator": "Buhler et al., Sections 3.1, 3.2, and 3.4"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/1407.4711",
    "locator": "Buhler et al., Sections 3.1, 3.2, and 3.4"
  },
  "models": [],
  "relations": [
    {
      "slug": "R455",
      "title": "The checked interval is 7/20 through 81/224, and equality at 7/20 remains open",
      "object_type": "claim",
      "relation": "supports",
      "direction": "outgoing"
    },
    {
      "slug": "R447",
      "title": "Exact replay of one 81/224 hint-matrix partition",
      "object_type": "artifact",
      "relation": "produced",
      "direction": "outgoing"
    },
    {
      "slug": "R448",
      "title": "Exact all-partitions certificate for the 81/224 hint-matrix value",
      "object_type": "artifact",
      "relation": "produced",
      "direction": "outgoing"
    },
    {
      "slug": "levine-two-player-seven-twentieths",
      "title": "levine two player seven twentieths",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}