{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1545",
  "content_hash": null,
  "slug": "five-cell-lattice-animal-plane-tiling-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 MathOverflow and Mathematics Stack Exchange pages have no solution. The source author reported in 2021 that the author of the four-cell theorem knew of no later progress, and no subsequent exact classification was found. Exact unresolved remainder: Prove that every five-element subset A of Z^2 tiles by lattice translations and square-lattice symmetries, or exhibit a specific five-element A and prove that no such tiling exists. A positive computational classification must state a finite reduction for arbitrarily separated cells and provide periodic fundamental-domain certificates for every reduced class; bounded-box enumeration alone is insufficient.",
  "relevance": "For Plane tilings by every five-cell lattice animal, 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 MathOverflow and Mathematics Stack Exchange pages have no solution. The source author reported in 2021 that the author of the four-cell theorem knew of no later progress, and no subsequent exact classification was found.\n\nExact unresolved remainder: Prove that every five-element subset A of Z^2 tiles by lattice translations and square-lattice symmetries, or exhibit a specific five-element A and prove that no such tiling exists. A positive computational classification must state a finite reduction for arbitrarily separated cells and provide periodic fundamental-domain certificates for every reduced class; bounded-box enumeration alone is insufficient.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://mathoverflow.net/questions/380490/does-every-5-celled-animal-tile-the-plane",
      "locator": "Full question, answers, and visible comments concerning Plane tilings by every five-cell lattice animal; checked 2026-08-01."
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://mathoverflow.net/questions/380490/does-every-5-celled-animal-tile-the-plane",
    "locator": "Full question, answers, and visible comments concerning Plane tilings by every five-cell lattice animal; checked 2026-08-01."
  },
  "relations": [
    {
      "slug": "R1311",
      "title": "Current checked status and unresolved remainder",
      "object_type": "claim",
      "relation": "supersedes",
      "direction": "outgoing"
    },
    {
      "slug": "five-cell-lattice-animal-plane-tiling",
      "title": "five cell lattice animal plane tiling",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}