{
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  "ref": "R1311",
  "content_hash": null,
  "slug": "five-cell-lattice-animal-plane-tiling-status-20260801",
  "type": "claim",
  "title": "Current checked status and unresolved remainder",
  "summary": "UNKNOWN as of 2026-07-27. 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.",
  "relevance": "Records the strongest checked neighboring results and the exact remainder future work must settle.",
  "relevance_source": "recorded",
  "body": "A dated independent review on 2026-08-01 checked the structured sources below, the complete visible source discussion, exact-title and equivalent-formulation searches, and the current TheoremDB corpus. On 2026-07-27 the Stack Exchange API reported zero answers, no accepted answer, and no closure for MathOverflow question 380490; comments settle only special shapes such as a 2 by 2 block plus one cell. Coppersmith's 1985 note proves the four-cell analogue even without reflections. The source records direct correspondence in 2021 confirming no known five-cell extension at that time. The linked Mathematics Stack Exchange question reports exhaustive tilings for all five-cell subsets of a 3 by 3 box and finite-region covers for a 4 by 4 box, without an all-animal proof. A TheoremDB search for disconnected polyominoes, five-cell animals, and lattice tiling universality found no duplicate.\n\nA complete resolution must satisfy: 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": "Dataset references and independent 2026-08-01 status search."
    },
    "missing": [
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  "formal_statement": null,
  "source": {
    "url": "https://mathoverflow.net/questions/380490/does-every-5-celled-animal-tile-the-plane",
    "locator": "Dataset references and independent 2026-08-01 status search."
  },
  "relations": [
    {
      "slug": "R1310",
      "title": "Complete the stated acceptance conditions",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
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    {
      "slug": "R1545",
      "title": "Dated status and exact unresolved remainder",
      "object_type": "claim",
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    {
      "slug": "five-cell-lattice-animal-plane-tiling",
      "title": "five cell lattice animal plane tiling",
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      "relation": "recorded_for",
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}