{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1525",
  "content_hash": null,
  "slug": "falconer-distance-conjecture-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: The linked 2025 preprint proves Falconer-type conclusions for selected function and set classes. It does not reach the unrestricted Hausdorff-dimension threshold d/2. Exact unresolved remainder: For every dimension d, prove positive measure of the distance set whenever a compact set has Hausdorff dimension greater than d/2, or construct a qualifying counterexample.",
  "relevance": "For Falconer distance conjecture, 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: The linked 2025 preprint proves Falconer-type conclusions for selected function and set classes. It does not reach the unrestricted Hausdorff-dimension threshold d/2.\n\nExact unresolved remainder: For every dimension d, prove positive measure of the distance set whenever a compact set has Hausdorff dimension greater than d/2, or construct a qualifying counterexample.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://arxiv.org/abs/2510.15118",
      "locator": "abstract and applications to selected Falconer-type classes"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/2510.15118",
    "locator": "abstract and applications to selected Falconer-type classes"
  },
  "relations": [
    {
      "slug": "R960",
      "title": "Current status and unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "outgoing"
    },
    {
      "slug": "falconer-distance-conjecture",
      "title": "falconer distance conjecture",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}