{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R449",
  "content_hash": null,
  "slug": "levine-artifact-three-block-best-response",
  "type": "artifact",
  "title": "Exact finite best-response enumerator",
  "summary": "A Gray-code integer enumerator checks 4,793,488 observed strings across seven truncations, returns zero best-response excess, and checks the depth-independent local score matrix.",
  "relevance": "For The value of Levine's two-player coin-index game, record levine-artifact-three-block-best-response (“Exact finite best-response enumerator”) supplies evidence or a replay used to check the packet. The record states: A Gray-code integer enumerator checks 4,793,488 observed strings across seven truncations, returns zero best-response excess, and checks the depth-independent local score matrix.",
  "relevance_source": "recorded",
  "body": "For each size, the program first forms the integer correlation table \\(C_{jk}\\), where \\(C_{jk}\\) counts strings \\(A\\) with \\(A_j=1\\) for which the fixed strategy chooses \\(k\\). Given an observed string \\(B\\), choosing coordinate \\(j\\) wins for exactly \\(\\sum_k B_k C_{jk}\\) strings \\(A\\). A Gray-code traversal updates all coordinate scores after each one-bit change in \\(B\\), and the program sums the exact maximum score over every \\(B\\).\n\nAll arithmetic is integral until the final reduced fractions are formed. The run covers \\(2^4+2^7+\\cdots+2^{22}=4{,}793{,}488\\) observed strings. For the first three sizes, a separate double loop over every ordered pair \\((A,B)\\) confirms the symmetric total. The program also constructs the local one-count matrix and checks the six nonmonochromatic advantage vectors used in the all-depth proof.",
  "status": "available",
  "evidence_grade": "executable",
  "scope": {
    "kind": "bounded",
    "statement": "every observed bit string and every response coordinate for the 1 through 7 block finite truncations",
    "bounds": {
      "blocks": {
        "min": 1,
        "max": 7
      },
      "finite_hat_count": {
        "min": 4,
        "max": 22
      },
      "candidate_response_coordinates": {
        "min": 4,
        "max": 22
      },
      "observed_strings_total": {
        "min": 4793488,
        "max": 4793488
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "partial",
    "kind": "python_exact_best_response_enumerator",
    "command": "python3 tools/levine_three_block_best_response.py --max-blocks 7",
    "entrypoint": "tools/levine_three_block_best_response.py",
    "runtime": "CPython 3.9.6, standard library only",
    "citation": {
      "locator": "tools/levine_three_block_best_response.py, source SHA-256 2129abca56fa00c9c4a9f81b7277e3662edaaafbe49fd70f9703122dc695a5c4"
    },
    "dependencies": [
      {
        "name": "CPython standard library",
        "license": "Python-2.0"
      }
    ],
    "outputs": {
      "stdout_sha256": "8608817224312c50baee47887ebcc7b1f5bfbb4e7fa48c293968e1b2032b90b1",
      "stdout_bytes": 3423,
      "all_truncations_are_self_best_responses": true,
      "best_response_excess": "0 for m=1,...,7",
      "observed_strings_total": 4793488,
      "local_one_count_matrix": "2,1,0/1,0,2/0,2,1",
      "all_six_local_advantage_vectors_checked": true,
      "closed_correlation_formula_checked_at_every_enumerated_depth": true,
      "direct_pair_cross_check_blocks": {
        "min": 1,
        "max": 3
      }
    },
    "runtime_seconds": 17.67,
    "missing": [
      "source"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": null,
    "locator": "tools/levine_three_block_best_response.py, source SHA-256 2129abca56fa00c9c4a9f81b7277e3662edaaafbe49fd70f9703122dc695a5c4"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R456",
      "title": "The truncated strategy is a best response to itself through seven blocks",
      "object_type": "claim",
      "relation": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "R452",
      "title": "Stress-test the all-depth response proof on blocks eight through twelve",
      "object_type": "attempt",
      "relation": "uses",
      "direction": "incoming"
    },
    {
      "slug": "R457",
      "title": "The three-block strategy is a best response to itself at every depth",
      "object_type": "claim",
      "relation": "tests",
      "direction": "outgoing"
    },
    {
      "slug": "levine-two-player-seven-twentieths",
      "title": "levine two player seven twentieths",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}