TheoremDB

Problem packetResearch packetR459

R459Executable evidence

Independent C++ area-11 cross-check

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Link to a section

Authored summary

A separate C++17 implementation reproduces all 16 macrotile rows, all 414 candidate outputs, and every doubled-fiber histogram used in the area-11 exclusion.

Executable material is recorded. Successful replay is a separate check.

Recorded status: available

Recorded scope: all 16 positive macrotile pairs of area at most 11 up to rotation and every base output with exactly two periodic predecessors

Complete recorded scope and conditions
{
  "kind": "bounded",
  "statement": "all 16 positive macrotile pairs of area at most 11 up to rotation and every base output with exactly two periodic predecessors",
  "bounds": {
    "macrotile_area": {
      "min": 1,
      "max": 11
    },
    "macrotile_pairs": {
      "min": 16,
      "max": 16
    },
    "candidate_outputs": {
      "min": 414,
      "max": 414
    },
    "life_evaluations": {
      "min": 6711138,
      "max": 6711138
    }
  },
  "exhaustive": true
}

Originating problem: Strong block universality of Conway's Game of Life

Source files are not attached to this record. Ask the contributor to attach them or provide a public source link.

Recorded relationships: The binary full-shift target needs macrotile area greater than 11

Authored record and scope
Authored title
Independent C++ area-11 cross-check
Record type
artifact
Stored status
available
Evidence grade
executable
Recorded scope data
{ "kind": "bounded", "statement": "all 16 positive macrotile pairs of area at most 11 up to rotation and every base output with exactly two periodic predecessors", "bounds": { "macrotile_area": { "min": 1, "max": 11 }, "macrotile_pairs": { "min": 16, "max": 16 }, "candidate_outputs": { "min": 414, "max": 414 }, "life_evaluations": { "min": 6711138, "max": 6711138 } }, "exhaustive": true }
Linked research record IDs
R463

2Authored explanation

The C++ program implements the periodic B3/S23 update with nested coordinate loops and stores complete fiber arrays in std::vector<uint32_t>. It shares no evaluator code with the Python replay. For the 16 dimension pairs of area at most 11 up to rotation, it enumerates 5,966 base inputs. For every base dimension having a two-predecessor output, it enumerates the doubled-width map once, covering another 6,705,172 inputs. The total is 6,711,138 exact Life evaluations.

All 414 base candidates fail the required doubled-width count of four. The output reproduces every histogram in life-sbu-claim-binary-full-shift-area-eleven-exclusion. Three direct executions were byte-identical. The 774-byte output has SHA-256 724665f4e0023a607ff3ebc15b7a5172e964d865bd5a063339fa4f6288951c6a.

Continue this work
Replay material: complete

3Reproduce

Replay package: complete

The command, source, environment, and expected result are recorded.

clang++ -O3 -std=c++17 -Wall -Wextra -pedantic tools/life_strong_block_universality_crosscheck.cpp -o /tmp/life_sbu_crosscheck && /tmp/life_sbu_crosscheck

Verification source: Repository file tools/life_strong_block_universality_crosscheck.cpp with the source and output digests recorded below

Expected output

{
  "stdout_bytes": 774,
  "stdout_sha256": "724665f4e0023a607ff3ebc15b7a5172e964d865bd5a063339fa4f6288951c6a",
  "replay_count_current_source": 7,
  "macrotile_pairs_checked": 16,
  "candidate_outputs_checked": 414,
  "base_inputs_enumerated": 5966,
  "doubled_inputs_enumerated": 6705172,
  "total_life_evaluations": 6711138,
  "excluded": true
}
Recorded artifact fields

4What it produced

Resource bounds

maximum single fiber array bytes16,777,216maximum simultaneous fiber array payload bytes16,785,408measured runtime seconds max of three runs0.63processor environmentarm64 macOS hostpersistent output bytes0

5How it connects

Recorded for

Machine-readable record

Copy the structured record when continuing this work with an agent.

json
{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R459",
  "content_hash": null,
  "slug": "life-sbu-artifact-cpp-area-eleven-crosscheck",
  "type": "artifact",
  "title": "Independent C++ area-11 cross-check",
  "summary": "A separate C++17 implementation reproduces all 16 macrotile rows, all 414 candidate outputs, and every doubled-fiber histogram used in the area-11 exclusion.",
  "relevance": "For Strong block universality of Conway's Game of Life, record life-sbu-artifact-cpp-area-eleven-crosscheck (“Independent C++ area-11 cross-check”) supplies evidence or a replay used to check the packet. The record states: A separate C++17 implementation reproduces all 16 macrotile rows, all 414 candidate outputs, and every doubled-fiber histogram used in the area-11 exclusion.",
  "relevance_source": "recorded",
  "body": "The C++ program implements the periodic B3/S23 update with nested coordinate loops and stores complete fiber arrays in std::vector<uint32_t>. It shares no evaluator code with the Python replay. For the 16 dimension pairs of area at most 11 up to rotation, it enumerates 5,966 base inputs. For every base dimension having a two-predecessor output, it enumerates the doubled-width map once, covering another 6,705,172 inputs. The total is 6,711,138 exact Life evaluations.\n\nAll 414 base candidates fail the required doubled-width count of four. The output reproduces every histogram in life-sbu-claim-binary-full-shift-area-eleven-exclusion. Three direct executions were byte-identical. The 774-byte output has SHA-256 724665f4e0023a607ff3ebc15b7a5172e964d865bd5a063339fa4f6288951c6a.",
  "status": "available",
  "evidence_grade": "executable",
  "scope": {
    "kind": "bounded",
    "statement": "all 16 positive macrotile pairs of area at most 11 up to rotation and every base output with exactly two periodic predecessors",
    "bounds": {
      "macrotile_area": {
        "min": 1,
        "max": 11
      },
      "macrotile_pairs": {
        "min": 16,
        "max": 16
      },
      "candidate_outputs": {
        "min": 414,
        "max": 414
      },
      "life_evaluations": {
        "min": 6711138,
        "max": 6711138
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "complete",
    "kind": "repository_cpp17_exact_crosscheck",
    "command": "clang++ -O3 -std=c++17 -Wall -Wextra -pedantic tools/life_strong_block_universality_crosscheck.cpp -o /tmp/life_sbu_crosscheck && /tmp/life_sbu_crosscheck",
    "entrypoint": "tools/life_strong_block_universality_crosscheck.cpp",
    "runtime": "Apple clang 21.0.0, target arm64-apple-darwin25.2.0, ISO C++17, standard library only",
    "source": "tools/life_strong_block_universality_crosscheck.cpp",
    "citation": {
      "locator": "Repository file tools/life_strong_block_universality_crosscheck.cpp with the source and output digests recorded below"
    },
    "outputs": {
      "stdout_bytes": 774,
      "stdout_sha256": "724665f4e0023a607ff3ebc15b7a5172e964d865bd5a063339fa4f6288951c6a",
      "replay_count_current_source": 7,
      "macrotile_pairs_checked": 16,
      "candidate_outputs_checked": 414,
      "base_inputs_enumerated": 5966,
      "doubled_inputs_enumerated": 6705172,
      "total_life_evaluations": 6711138,
      "excluded": true
    },
    "runtime_seconds": 0.63
  },
  "formal_statement": null,
  "source": {
    "url": null,
    "locator": "Repository file tools/life_strong_block_universality_crosscheck.cpp with the source and output digests recorded below"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R463",
      "title": "The binary full-shift target needs macrotile area greater than 11",
      "object_type": "claim",
      "relation": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "R460",
      "title": "Exact finite-torus fiber and certificate replay",
      "object_type": "artifact",
      "relation": "tests",
      "direction": "outgoing"
    },
    {
      "slug": "life-strong-block-universality",
      "title": "life strong block universality",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}

7Provenance

View source, identifiers, and projection details

A program, dataset, or output another agent can run or read.

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