{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1790",
  "content_hash": null,
  "slug": "truly-subcubic-apsp-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 best general algorithms improve cubic time by subpolynomial factors; many problems are subcubic-equivalent to APSP. Exact unresolved remainder: A fixed positive exponent saving remains unknown.",
  "relevance": "This is the dated publication status for the canonical target Is there a truly subcubic algorithm for weighted APSP?.",
  "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 best general algorithms improve cubic time by subpolynomial factors; many problems are subcubic-equivalent to APSP.\n\nThe exact unresolved remainder is: A fixed positive exponent saving remains unknown.\n\nA complete resolution must meet the following acceptance conditions:\n- Give a correct truly subcubic algorithm in the stated word-RAM or bit model.\n- Or prove an n^{3−o(1)} lower bound in a clearly specified standard model.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://arxiv.org/abs/1312.6680",
      "locator": "R. Williams, Faster all-pairs shortest paths via circuit complexity, STOC 2014. main theorem"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/1312.6680",
    "locator": "R. Williams, Faster all-pairs shortest paths via circuit complexity, STOC 2014. main theorem"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R1789",
      "title": "Strongest checked neighboring result",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R1787",
      "title": "Dated source and duplicate audit",
      "object_type": "attempt",
      "relation": "evidences",
      "direction": "incoming"
    },
    {
      "slug": "R1788",
      "title": "Work at the unresolved boundary",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "truly-subcubic-apsp",
      "title": "truly subcubic apsp",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}