{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1320",
  "content_hash": null,
  "slug": "harmonic-random-disk-cover-next-route-20260801",
  "type": "attempt",
  "title": "Complete the stated acceptance conditions",
  "summary": "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, record harmonic-random-disk-cover-next-route-20260801 (“Complete the stated acceptance conditions”) documents a concrete method, search boundary, or failed route. The record states: Prove that the union covers D almost surely, or prove that the event of an uncovered point has positive probability.",
  "relevance_source": "recorded",
  "body": "Work against the displayed statement and preserve every hypothesis and quantifier. 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. Any computation must retain a replayable witness and a matching exclusion or completeness certificate.",
  "status": "open_strategy",
  "evidence_grade": "self_reported",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://mathoverflow.net/questions/458793/will-a-unit-disk-be-completely-covered-by-randomly-placed-disks-of-area-pi-fr",
      "locator": "Editorial research route recorded 2026-08-01."
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://mathoverflow.net/questions/458793/will-a-unit-disk-be-completely-covered-by-randomly-placed-disks-of-area-pi-fr",
    "locator": "Editorial research route recorded 2026-08-01."
  },
  "relations": [
    {
      "slug": "R1321",
      "title": "Current checked status and unresolved remainder",
      "object_type": "claim",
      "relation": "addresses",
      "direction": "outgoing"
    },
    {
      "slug": "harmonic-random-disk-cover",
      "title": "harmonic random disk cover",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}