{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R460",
  "content_hash": null,
  "slug": "life-sbu-artifact-finite-torus-replay",
  "type": "artifact",
  "title": "Exact finite-torus fiber and certificate replay",
  "summary": "A deterministic Python program enumerates 7,038,802 periodic Life inputs, checks the area-11 binary-full-shift obstruction, and verifies 126 explicit 6 by 6 alternative predecessors for the 3 by 3 singleton fibers.",
  "relevance": "For Strong block universality of Conway's Game of Life, record life-sbu-artifact-finite-torus-replay (“Exact finite-torus fiber and certificate replay”) supplies evidence or a replay used to check the packet. The record states: A deterministic Python program enumerates 7,038,802 periodic Life inputs, checks the area-11 binary-full-shift obstruction, and verifies 126 explicit 6 by 6 alternative predecessors for the 3 by 3 singleton fibers.",
  "relevance_source": "recorded",
  "body": "The program evaluates the B3/S23 rule directly on each finite torus. Neighbor coordinates retain multiplicity, which is required when a fundamental period is 1 or 2. A coordinate-set implementation independently agrees with the main evaluator for every state on each listed torus of area at most 12. A 5 by 5 blinker supplies a separate conventional-rule check.\n\nThe general fiber survey covers 29 listed tori and 2,844,494 inputs. The stable row data has SHA-256 af7a24b81711a0fd1f49be2aabea8fa0d350e10456938c87aa768779d9a1fca7. The binary-full-shift screen adds the 2 by 1 and 2 by 11 tori, and covers all 16 dimension pairs of area at most 11 up to rotation. Its stable data has SHA-256 cd80fc067571d23ba752537d4dd65f33e0f17c167de684d607e3746be7cbe574. Across both stages, the 31 cached fiber tables enumerate 7,038,802 periodic inputs.\n\nThe 3 by 3 torus offers a useful calibration. Its 126 singleton fibers are exactly the weight-four configurations, each fixed by Life. Z3 5.0.0 was used once to find a distinct 6 by 6 periodic predecessor for every lifted output. The replay depends only on the stored integer certificates and the Python standard library. It verifies all 126 witnesses, proving that none of those finite-torus singleton fibers is globally singleton. The canonical certificate encoding is 2,193 bytes with SHA-256 e2f87cdbde0e87c44d2a86c38d63a9029bdf2c45b073bbe23d690fb085180dbc.",
  "status": "available",
  "evidence_grade": "executable",
  "scope": {
    "kind": "bounded",
    "statement": "31 computed fiber tables, all 16 macrotile pairs of area at most 11 up to rotation, and all 126 singleton fibers on the 3 by 3 torus",
    "bounds": {
      "fiber_tables": {
        "min": 31,
        "max": 31
      },
      "enumerated_inputs": {
        "min": 7038802,
        "max": 7038802
      },
      "maximum_enumerated_torus_area": {
        "min": 22,
        "max": 22
      },
      "binary_full_shift_macrocell_area": {
        "min": 1,
        "max": 11
      },
      "three_by_three_certificates": {
        "min": 126,
        "max": 126
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "complete",
    "kind": "repository_python_exact_computation",
    "command": "python3 tools/life_strong_block_universality_replay.py",
    "entrypoint": "tools/life_strong_block_universality_replay.py",
    "runtime": "CPython 3.9.6, standard library only",
    "source": "tools/life_strong_block_universality_replay.py",
    "citation": {
      "locator": "Repository file tools/life_strong_block_universality_replay.py with the source and output digests recorded below"
    },
    "outputs": {
      "stdout_bytes": 7704,
      "stdout_sha256": "ea175ff061b23d407734deb5809b876a7b30aeeb3a1353bd0967c7e442daeaf4",
      "replay_count_current_source": 1,
      "survey_tori_checked": 29,
      "survey_inputs_checked": 2844494,
      "fiber_tables_computed": 31,
      "fiber_inputs_enumerated": 7038802,
      "stable_results_bytes": 4040,
      "stable_results_sha256": "af7a24b81711a0fd1f49be2aabea8fa0d350e10456938c87aa768779d9a1fca7",
      "binary_full_shift_checks_bytes": 2843,
      "binary_full_shift_checks_sha256": "cd80fc067571d23ba752537d4dd65f33e0f17c167de684d607e3746be7cbe574",
      "three_by_three_singleton_fibers": 126,
      "three_by_three_alternative_certificates": 126,
      "three_by_three_certificate_bytes": 2193,
      "three_by_three_certificate_sha256": "e2f87cdbde0e87c44d2a86c38d63a9029bdf2c45b073bbe23d690fb085180dbc"
    },
    "runtime_seconds": 85.97
  },
  "formal_statement": null,
  "source": {
    "url": null,
    "locator": "Repository file tools/life_strong_block_universality_replay.py with the source and output digests recorded below"
  },
  "relations": [
    {
      "slug": "R463",
      "title": "The binary full-shift target needs macrotile area greater than 11",
      "object_type": "claim",
      "relation": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "R459",
      "title": "Independent C++ area-11 cross-check",
      "object_type": "artifact",
      "relation": "tests",
      "direction": "incoming"
    },
    {
      "slug": "R461",
      "title": "Extend the binary full-shift periodic-count screen",
      "object_type": "attempt",
      "relation": "uses",
      "direction": "incoming"
    },
    {
      "slug": "life-strong-block-universality",
      "title": "life strong block universality",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}