{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1642",
  "content_hash": null,
  "slug": "matrix-multiplication-exponent-two-claim-status-20260801",
  "type": "claim",
  "title": "Current status and exact unresolved remainder",
  "summary": "OPEN as checked on 2026-08-01. Strongest checked neighboring result: The current located upper bound is ω<2.371339 and the trivial information-size lower bound is 2. Exact unresolved remainder: Closing any positive part of the gap between 2 and 2.371339 remains open.",
  "relevance": "This is the dated publication status for the canonical target Does the matrix-multiplication exponent equal two?.",
  "relevance_source": "recorded",
  "body": "The problem was checked as open on 2026-08-01.\n\nThe strongest neighboring result found in the cited sources is: The current located upper bound is ω<2.371339 and the trivial information-size lower bound is 2.\n\nThe exact unresolved remainder is: Closing any positive part of the gap between 2 and 2.371339 remains open.\n\nA complete resolution must meet the following acceptance conditions:\n- Give algorithms proving ω≤2+ε for every ε>0.\n- Or prove a lower bound ω≥2+δ for some fixed δ>0.",
  "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"
  },
  "relations": [
    {
      "slug": "R1641",
      "title": "Strongest checked neighboring result",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R1639",
      "title": "Dated source and duplicate audit",
      "object_type": "attempt",
      "relation": "evidences",
      "direction": "incoming"
    },
    {
      "slug": "R1640",
      "title": "Work at the unresolved boundary",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "matrix-multiplication-exponent-two",
      "title": "matrix multiplication exponent two",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}