{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R461",
  "content_hash": null,
  "slug": "life-sbu-attempt-extend-periodic-count-screen",
  "type": "attempt",
  "title": "Extend the binary full-shift periodic-count screen",
  "summary": "Use exact SAT or transfer methods to test macrocell areas 12 through 18 against several periodic-point counts for the constant binary-full-shift target.",
  "relevance": "For Strong block universality of Conway's Game of Life, record life-sbu-attempt-extend-periodic-count-screen (“Extend the binary full-shift periodic-count screen”) documents a concrete method, search boundary, or failed route. The record states: Use exact SAT or transfer methods to test macrocell areas 12 through 18 against several periodic-point counts for the constant binary-full-shift target.",
  "relevance_source": "recorded",
  "body": "Continue the constant-map test with the binary full shift. For each positive \\((m,n)\\) of area 12 through 18, enumerate or symbolically represent every \\(m\\)-by-\\(n\\) output with exactly two periodic predecessors. For each survivor, count the lifted fiber on \\(2m\\)-by-\\(n\\), \\(m\\)-by-\\(2n\\), and \\(2m\\)-by-\\(2n\\) tori. The required counts are 4, 4, and 16.\n\nA practical implementation should encode each requested output fiber separately in SAT and enumerate models with blocking clauses, or use row transfer when one dimension is small. Store explicit witnesses for count overflow and independently verify them with the standard-library evaluator. For a claimed exact count, retain a solver-checkable enumeration certificate rather than a solver summary.\n\nStop after every dimension pair through area 18 has either failed one required count or produced a survivor with certified counts. A survivor should trigger the next periodic tests \\((p,q)=(3,1),(1,3),(2,3)\\). It does not establish a conjugacy because aperiodic points and local invertibility remain unchecked. A full elimination through area 18 would extend the present lower bound. Any survivor would identify the first macrocell worth a direct conjugacy or obstruction study.",
  "status": "next_experiment",
  "evidence_grade": "self_reported",
  "scope": {
    "kind": "bounded",
    "statement": "planned periodic-fiber count screen for binary-full-shift constant-map simulations with macrotile area 12 through 18",
    "bounds": {
      "macrotile_area": {
        "min": 12,
        "max": 18
      },
      "period_multiplier": {
        "min": 1,
        "max": 3
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "locator": "Continuation plan based on life-sbu-claim-periodic-fiber-count-test and the exact replay boundary in life-sbu-artifact-finite-torus-replay"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": null,
    "locator": "Continuation plan based on life-sbu-claim-periodic-fiber-count-test and the exact replay boundary in life-sbu-artifact-finite-torus-replay"
  },
  "relations": [
    {
      "slug": "R460",
      "title": "Exact finite-torus fiber and certificate replay",
      "object_type": "artifact",
      "relation": "uses",
      "direction": "outgoing"
    },
    {
      "slug": "R464",
      "title": "Semiweak universality is proved and strong universality remains open",
      "object_type": "claim",
      "relation": "attempts",
      "direction": "outgoing"
    },
    {
      "slug": "life-strong-block-universality",
      "title": "life strong block universality",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}