{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R450",
  "content_hash": null,
  "slug": "levine-artifact-three-block-replay",
  "type": "artifact",
  "title": "Exact replay of the three-block 7/20 strategy",
  "summary": "A standard-library Python replay finds 15 winning local pairs out of 36 and verifies the finite formula \\(7/20-1/(10\\cdot16^m)\\) for \\(1\\le m\\le12\\).",
  "relevance": "For The value of Levine's two-player coin-index game, record levine-artifact-three-block-replay (“Exact replay of the three-block 7/20 strategy”) supplies evidence or a replay used to check the packet. The record states: A standard-library Python replay finds 15 winning local pairs out of 36 and verifies the finite formula \\(7/20-1/(10\\cdot16^m)\\) for \\(1\\le m\\le12\\).",
  "relevance_source": "recorded",
  "body": "The program implements the published symmetric local map in two independent representations: string tuples and three-bit integers. Both enumerate the same set of \\(15\\) winning ordered pairs. The SHA-256 digest of the sorted `left,right` pair list is `16b0e5ef3f81f12c465fee9eb10e3725800f1c86a095e8b3343fc19c6537eb5c`.\n\nThe replay then performs the exact geometric calculation for the infinite recursive strategy. For a finite truncation with \\(m\\) scanned blocks, it uses coordinate \\(3m+1\\) when every scanned block is monochromatic. The resulting probability is\n\\[\n\\frac7{20}-\\frac{1}{10\\cdot16^m}.\n\\]\nThe run checks this identity for every \\(m\\) from 1 through 12. The endpoints are \\(11/32\\) at four hats and \\(197032483697459/562949953421312\\) at 37 hats.",
  "status": "available",
  "evidence_grade": "executable",
  "scope": {
    "kind": "bounded",
    "statement": "all 36 ordered pairs of nonmonochromatic three-bit words and finite truncations with 1 through 12 blocks",
    "bounds": {
      "ordered_local_word_pairs": {
        "min": 36,
        "max": 36
      },
      "blocks": {
        "min": 1,
        "max": 12
      },
      "finite_hat_count": {
        "min": 4,
        "max": 37
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "partial",
    "kind": "python_exact_rational_replay",
    "command": "python3 tools/levine_three_block_replay.py --max-blocks 12",
    "entrypoint": "tools/levine_three_block_replay.py",
    "runtime": "CPython 3.9.6, standard library only",
    "citation": {
      "locator": "tools/levine_three_block_replay.py, source SHA-256 3b5e03d375fb160e18ca48eb2c1e436f253858db4a68f5e1efead9d62bdced46"
    },
    "dependencies": [
      {
        "name": "CPython standard library",
        "license": "Python-2.0"
      }
    ],
    "outputs": {
      "stdout_sha256": "6cf79532b602b515d20ac3138e3b410195ffa43451cf46e5a0e5be4266962c81",
      "stdout_bytes": 2515,
      "winning_pairs_sha256": "16b0e5ef3f81f12c465fee9eb10e3725800f1c86a095e8b3343fc19c6537eb5c",
      "winning_word_pairs": 15,
      "ordered_word_pairs": 36,
      "infinite_win_probability": "7/20",
      "checked_blocks": {
        "min": 1,
        "max": 12
      }
    },
    "runtime_seconds": 0.05,
    "missing": [
      "source"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": null,
    "locator": "tools/levine_three_block_replay.py, source SHA-256 3b5e03d375fb160e18ca48eb2c1e436f253858db4a68f5e1efead9d62bdced46"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R458",
      "title": "A symmetric recursive three-block strategy wins with probability exactly 7/20",
      "object_type": "claim",
      "relation": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "levine-two-player-seven-twentieths",
      "title": "levine two player seven twentieths",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}