{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1639",
  "content_hash": null,
  "slug": "matrix-multiplication-exponent-two-attempt-dated-source-audit",
  "type": "attempt",
  "title": "Dated source and duplicate audit",
  "summary": "The exact target, equivalent terminology, and 2025-2026 status evidence were checked on 2026-08-01. Strongest checked result: The current located upper bound is ω<2.371339 and the trivial information-size lower bound is 2. Unresolved remainder: Closing any positive part of the gap between 2 and 2.371339 remains open.",
  "relevance": "Documents why Does the matrix-multiplication exponent equal two? was treated as a distinct open target on 2026-08-01.",
  "relevance_source": "recorded",
  "body": "The audit ran on 2026-08-01 across the cited primary literature and problem collections, Crossref, arXiv, and stable publisher records, TheoremDB published, prospecting, packet, formal, and retired corpus. It checked the exact statement, its named or normalized variants, recent status evidence, and the controlled TheoremDB corpus.\n\nQueries included:\n- matrix multiplication exponent omega equals 2 open 2026 best bound\n- current best omega 2.371339 ADVXXZ 2025\n\nThe exact target, equivalent terminology, and 2025-2026 status evidence were checked on 2026-08-01. Strongest checked result: The current located upper bound is ω<2.371339 and the trivial information-size lower bound is 2. Unresolved remainder: Closing any positive part of the gap between 2 and 2.371339 remains open.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.1137/1.9781611978322.63",
      "locator": "J. Alman, R. Duan, V. Vassilevska Williams, Y. Xu, Z. Xu, and R. Zhou, “More Asymmetry Yields Faster Matrix Multiplication,” Proceedings of SODA 2025, 2005–2039. abstract and square-matrix exponent theorem"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1137/1.9781611978322.63",
    "locator": "J. Alman, R. Duan, V. Vassilevska Williams, Y. Xu, Z. Xu, and R. Zhou, “More Asymmetry Yields Faster Matrix Multiplication,” Proceedings of SODA 2025, 2005–2039. abstract and square-matrix exponent theorem"
  },
  "relations": [
    {
      "slug": "R1642",
      "title": "Current status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "matrix-multiplication-exponent-two",
      "title": "matrix multiplication exponent two",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}