{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R468",
  "content_hash": null,
  "slug": "life6-attempt-primary-literature-audit",
  "type": "attempt",
  "title": "Published precursor counts use a different finite-window convention",
  "summary": "The located literature supplies row-wise counting methods and hardness results, while the fixed-dead same-size value does not appear there.",
  "relevance": "This records a line of attack on the target problem, including what it establishes and where it stops.",
  "relevance_source": "derived",
  "body": "Beer gives an incremental row-aggregation algorithm for exact precursor counts in two-dimensional cellular automata and computes full precursor-count distributions for Life targets through side five. His finite-window convention assigns an \\((n+2)\\) by \\((n+2)\\) precursor to an \\(n\\) by \\(n\\) target. The free one-cell border can influence the target. For example, Beer reports 6,272,107,655,484 precursors for the all-dead 5 by 5 target. Under the present question's same-size fixed-dead convention, the corresponding count is 28,156. The published distribution therefore does not settle \\(P_6\\).\n\nSalo and Törmä study Life preimages on the infinite plane. Their 2022 paper proves results about finite patterns with no predecessors and unique-predecessor structure. Their later work proves coNP-completeness for orphan recognition and computational universality of one backward step. These results explain why broad predecessor questions can be difficult, while giving no table for this bounded map.\n\nA focused search of these primary sources and their cited precursor-counting work found no published value for the maximum fiber of the 6 by 6 same-size fixed-dead map. The novelty statement remains a search report. The exact value in this entry rests on the self-contained certificate.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": {
    "kind": "bounded",
    "statement": "primary sources on Game of Life precursor counting and one-step preimage complexity, checked for the same-size 6 by 6 fixed-dead maximum",
    "bounds": {
      "audit_date": {
        "min": 20260725,
        "max": 20260725
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.1063/1.5006143",
      "locator": "Randall D. Beer, Computing Aggregate Properties of Preimages for 2D Cellular Automata, Chaos 27, 111104 (2017), Sections III and IV; Ville Salo and Ilkka Törmä, What Can Oracles Teach Us About the Ultimate Fate of Life?, ICALP 2022; Salo and Törmä, Structure and Computability of Preimages in the Game of Life, Theoretical Computer Science 1042 (2025), 115237"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1063/1.5006143",
    "locator": "Randall D. Beer, Computing Aggregate Properties of Preimages for 2D Cellular Automata, Chaos 27, 111104 (2017), Sections III and IV; Ville Salo and Ilkka Törmä, What Can Oracles Teach Us About the Ultimate Fate of Life?, ICALP 2022; Salo and Törmä, Structure and Computability of Preimages in the Game of Life, Theoretical Computer Science 1042 (2025), 115237"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R469",
      "title": "The exact maximum preimage multiplicity is 1,093,273",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "life-six-preimage-multiplicity",
      "title": "life six preimage multiplicity",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}