{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1404",
  "content_hash": null,
  "slug": "borsuk-conjecture-in-four-dimensions-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 regular four-simplex gives b(4)≥5, while the current checked upper bound is b(4)≤8. Unresolved remainder: Determine whether b(4)=5; equivalently, prove five smaller-diameter parts always suffice or construct a unit-diameter set requiring at least six.",
  "relevance": "Documents why Borsuk’s conjecture in four dimensions 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- Borsuk number R4 exact value\n- Borsuk conjecture dimension four five colors diameter graph\n- b(4) upper bound 8 Tolmachev Voronov\n\nThe exact target, equivalent terminology, and 2025-2026 status evidence were checked on 2026-08-01. Strongest checked result: The regular four-simplex gives b(4)≥5, while the current checked upper bound is b(4)≤8. Unresolved remainder: Determine whether b(4)=5; equivalently, prove five smaller-diameter parts always suffice or construct a unit-diameter set requiring at least six.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.48550/arXiv.2605.19068",
      "locator": "A. Tolmachev and V. Voronov, “Reducing the upper bound for the Borsuk number in R⁴ to 8,” arXiv:2605.19068 (2026). abstract and main constructions"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.48550/arXiv.2605.19068",
    "locator": "A. Tolmachev and V. Voronov, “Reducing the upper bound for the Borsuk number in R⁴ to 8,” arXiv:2605.19068 (2026). abstract and main constructions"
  },
  "relations": [
    {
      "slug": "R1407",
      "title": "Current status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "borsuk-conjecture-in-four-dimensions",
      "title": "borsuk conjecture in four dimensions",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}