{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1787",
  "content_hash": null,
  "slug": "truly-subcubic-apsp-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 best general algorithms improve cubic time by subpolynomial factors; many problems are subcubic-equivalent to APSP. Unresolved remainder: A fixed positive exponent saving remains unknown.",
  "relevance": "Documents why Is there a truly subcubic algorithm for weighted APSP? 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- truly subcubic APSP open problem 2026\n- weighted all pairs shortest paths n 3 epsilon\n\nThe exact target, equivalent terminology, and 2025-2026 status evidence were checked on 2026-08-01. Strongest checked result: The best general algorithms improve cubic time by subpolynomial factors; many problems are subcubic-equivalent to APSP. Unresolved remainder: A fixed positive exponent saving remains unknown.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "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": "R1790",
      "title": "Current status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "truly-subcubic-apsp",
      "title": "truly subcubic apsp",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}