{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1590",
  "content_hash": null,
  "slug": "harmonic-random-disk-cover-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 comments establish almost-sure coverage of each fixed point and zero area of the uncovered set. They do not establish complete coverage of the uncountable disk, and the exact critical sequence was not settled in the checked random-covering literature. Exact unresolved remainder: Prove that the union covers D almost surely, or prove that the event of an uncovered point has positive probability. A computer-assisted argument must supply certified finite-net bounds and a rigorous passage that controls holes between net points and the boundary for the infinite tail.",
  "relevance": "For Complete coverage by random disks at the harmonic scale, 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 comments establish almost-sure coverage of each fixed point and zero area of the uncovered set. They do not establish complete coverage of the uncountable disk, and the exact critical sequence was not settled in the checked random-covering literature.\n\nExact unresolved remainder: Prove that the union covers D almost surely, or prove that the event of an uncovered point has positive probability. A computer-assisted argument must supply certified finite-net bounds and a rigorous passage that controls holes between net points and the boundary for the infinite tail.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://doi.org/10.1007/s00440-022-01182-5",
      "locator": "abstract and limit theorems for the coverage threshold R_n of n uniform centers with common radius"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1007/s00440-022-01182-5",
    "locator": "abstract and limit theorems for the coverage threshold R_n of n uniform centers with common radius"
  },
  "relations": [
    {
      "slug": "R1321",
      "title": "Current checked status and unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "outgoing"
    },
    {
      "slug": "harmonic-random-disk-cover",
      "title": "harmonic random disk cover",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}