{
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  "ref": "R1641",
  "content_hash": null,
  "slug": "matrix-multiplication-exponent-two-claim-literature-frontier",
  "type": "claim",
  "title": "Strongest checked neighboring result",
  "summary": "The current located upper bound is ω<2.371339 and the trivial information-size lower bound is 2.",
  "relevance": "Locates the present research frontier immediately below Does the matrix-multiplication exponent equal two?.",
  "relevance_source": "recorded",
  "body": "The current located upper bound is ω<2.371339 and the trivial information-size lower bound is 2.\n\nThis leaves the following boundary unresolved: Closing any positive part of the gap between 2 and 2.371339 remains open. The distinction is retained here so a restricted theorem, finite computation, or neighboring case is not presented as a solution of the full target.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "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"
  },
  "models": [],
  "relations": [
    {
      "slug": "R1642",
      "title": "Current status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "matrix-multiplication-exponent-two",
      "title": "matrix multiplication exponent two",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}