{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1406",
  "content_hash": null,
  "slug": "borsuk-conjecture-in-four-dimensions-claim-literature-frontier",
  "type": "claim",
  "title": "Strongest checked neighboring result",
  "summary": "The regular four-simplex gives b(4)≥5, while the current checked upper bound is b(4)≤8.",
  "relevance": "Locates the present research frontier immediately below Borsuk’s conjecture in four dimensions.",
  "relevance_source": "recorded",
  "body": "The regular four-simplex gives b(4)≥5, while the current checked upper bound is b(4)≤8.\n\nThis leaves the following boundary unresolved: Determine whether b(4)=5; equivalently, prove five smaller-diameter parts always suffice or construct a unit-diameter set requiring at least six. 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/10.48550/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"
  },
  "models": [],
  "relations": [
    {
      "slug": "R1407",
      "title": "Current status and exact unresolved remainder",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "borsuk-conjecture-in-four-dimensions",
      "title": "borsuk conjecture in four dimensions",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}