{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1616",
  "content_hash": null,
  "slug": "kakeya-conjecture-in-dimensions-at-least-four-status-packet-quality-20260801",
  "type": "claim",
  "title": "Dated status and exact unresolved remainder",
  "summary": "Unresolved in this packet after the dated source check. Strongest checked result: Wang and Zahl prove the three-dimensional Kakeya conjecture. Guth's 2026 survey explains that proof and identifies dimension four as the next unresolved case; dimensions at least four remain open. Exact unresolved remainder: Prove full Hausdorff dimension for every Kakeya set in every dimension n at least 4, or construct a Kakeya set in one such dimension with dimension below n.",
  "relevance": "For Kakeya conjecture in dimensions at least four, this successor gives readable dated status prose and the exact remaining research boundary.",
  "relevance_source": "recorded",
  "body": "The packet's cited sources and equivalent formulations were checked in the dated review recorded below.\n\nStrongest checked result: Wang and Zahl prove the three-dimensional Kakeya conjecture. Guth's 2026 survey explains that proof and identifies dimension four as the next unresolved case; dimensions at least four remain open.\n\nExact unresolved remainder: Prove full Hausdorff dimension for every Kakeya set in every dimension n at least 4, or construct a Kakeya set in one such dimension with dimension below n.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://arxiv.org/abs/2502.17655",
      "locator": "Theorem 1.1 on page 3"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/2502.17655",
    "locator": "Theorem 1.1 on page 3"
  },
  "relations": [
    {
      "slug": "R1088",
      "title": "Current status and unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "outgoing"
    },
    {
      "slug": "kakeya-conjecture-in-dimensions-at-least-four",
      "title": "kakeya conjecture in dimensions at least four",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}