{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1096",
  "content_hash": null,
  "slug": "life-horizontal-line-weak-vanishing-claim-status-20260731",
  "type": "claim",
  "title": "Current status and unresolved remainder",
  "summary": "UNKNOWN as of 2026-07-31. The source reports that line lengths through 1000 fail to weakly vanish and gives glider-based heuristics for large lengths. The answer does not prove persistence for every n or exhibit a weakly vanishing n. Exhibit an integer n>=25 and prove that each fixed cell is eventually permanently dead, or prove that every n>=25 leaves some fixed cell alive at arbitrarily large times.",
  "relevance": "Defines the dated frontier and the exact remainder that research on this problem must resolve.",
  "relevance_source": "recorded",
  "body": "UNKNOWN as of 2026-07-31. The source reports that line lengths through 1000 fail to weakly vanish and gives glider-based heuristics for large lengths. The answer does not prove persistence for every n or exhibit a weakly vanishing n.\n\nA complete resolution must satisfy this condition: Exhibit an integer n>=25 and prove that each fixed cell is eventually permanently dead, or prove that every n>=25 leaves some fixed cell alive at arbitrarily large times.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://mathoverflow.net/questions/288423/vanishing-line-on-conways-game-of-life",
      "locator": "See dataset.references[0] for the exact external source and locator."
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://mathoverflow.net/questions/288423/vanishing-line-on-conways-game-of-life",
    "locator": "See dataset.references[0] for the exact external source and locator."
  },
  "relations": [
    {
      "slug": "R1095",
      "title": "Resolve the stated acceptance condition",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "life-horizontal-line-weak-vanishing",
      "title": "life horizontal line weak vanishing",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}