{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R464",
  "content_hash": null,
  "slug": "life-sbu-claim-current-status",
  "type": "claim",
  "title": "Semiweak universality is proved and strong universality remains open",
  "summary": "Salo and Törmä prove that Life is semiweakly universal and leave strong block universality open. This packet derives a periodic-fiber count test and excludes macrocell area at most 11 for one required target, the constant map from the binary full shift.",
  "relevance": "For Strong block universality of Conway's Game of Life, record life-sbu-claim-current-status (“Semiweak universality is proved and strong universality remains open”) records a bound, answer, status fact, or structural consequence. The record states: Salo and Törmä prove that Life is semiweakly universal and leave strong block universality open.",
  "relevance_source": "recorded",
  "body": "The primary paper introduces weak, semiweak, and strong simulation for block maps. Its circuit-system block map is effectively strongly universal, while Theorem 4 proves that Conway's Game of Life is semiweakly universal. Question 2 asks whether the Life simulation can be made strong, which requires the selected preimage map to be bijective and hence to contain no extraneous Life preimages.\n\nThe focused search dated 2026-07-28 found no later source answering that exact block-map question. The bounded result in this packet tests a necessary consequence of strong universality against every macrotile dimension of area at most 11. It does not produce a universal construction or a counterexample block map, so the canonical problem remains open.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "family",
    "statement": "the published semiweak-universality theorem, the exact strong block-map question, and the bounded progress recorded in this packet",
    "family": "one-step block-map simulations by Conway's Game of Life"
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://doi.org/10.1016/j.tcs.2025.115237",
      "locator": "Ville Salo and Ilkka Törmä, Structure and computability of preimages in the Game of Life, Theoretical Computer Science 1042 (2025), 115237, Definitions 4-5, Theorem 4, and Question 2"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1016/j.tcs.2025.115237",
    "locator": "Ville Salo and Ilkka Törmä, Structure and computability of preimages in the Game of Life, Theoretical Computer Science 1042 (2025), 115237, Definitions 4-5, Theorem 4, and Question 2"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R462",
      "title": "Primary-source audit separates three meanings of strong universality",
      "object_type": "attempt",
      "relation": "supports",
      "direction": "incoming"
    },
    {
      "slug": "R463",
      "title": "The binary full-shift target needs macrotile area greater than 11",
      "object_type": "claim",
      "relation": "supports",
      "direction": "incoming"
    },
    {
      "slug": "R461",
      "title": "Extend the binary full-shift periodic-count screen",
      "object_type": "attempt",
      "relation": "attempts",
      "direction": "incoming"
    },
    {
      "slug": "life-strong-block-universality",
      "title": "life strong block universality",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}