{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R766",
  "content_hash": null,
  "slug": "tc114-artifact-exact-verifier",
  "type": "artifact",
  "title": "Exact verifier for a proposed representation",
  "summary": "A standard-library Python program checks the cube identity, the height cap, and the necessary residues using arbitrary-precision integers.",
  "relevance": "For A bounded three-cubes search for 114, record tc114-artifact-exact-verifier (“Exact verifier for a proposed representation”) supplies evidence or a replay used to check the packet. The record states: A standard-library Python program checks the cube identity, the height cap, and the necessary residues using arbitrary-precision integers.",
  "relevance_source": "recorded",
  "body": "Save the source lines as `verify.py`. Running `python3 verify.py` performs deterministic self-tests. Running\n```\npython3 verify.py X Y Z\n```\nchecks any proposed integer triple. The program accepts the triple only when its exact cube sum equals 114 and its maximum absolute coordinate is at most \\(10^{20}\\). Python integers are arbitrary precision, so the calculation has no overflow or rounding step.\n\nThe residue test is reported separately. A genuine solution automatically passes it, while acceptance depends only on the exact equation and height definition.",
  "status": "available",
  "evidence_grade": "executable",
  "scope": {
    "kind": "bounded",
    "statement": "any supplied integer triple checked against target 114 and height at most 10^20",
    "bounds": {
      "height": {
        "min": 0,
        "max": 100000000000000000000
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "partial",
    "kind": "inline_python_computation",
    "entrypoint": "join source_lines with newline and run with python3; pass X Y Z as decimal command-line arguments to check a proposed triple",
    "runtime": "CPython 3, standard library only",
    "citation": {
      "url": "https://doi.org/10.1073/pnas.2022377118",
      "locator": "Inline Python verifier written and executed by TheoremDB entry research on 2026-07-25"
    },
    "inline_source": [
      "import sys",
      "TARGET = 114",
      "HEIGHT_LIMIT = 10**20",
      "ALLOWED_MOD9 = {2, 5, 8}",
      "",
      "def report(x, y, z):",
      "    values = (x, y, z)",
      "    cube_sum = sum(v**3 for v in values)",
      "    height = max(abs(v) for v in values)",
      "    equation = cube_sum == TARGET",
      "    within_height = height <= HEIGHT_LIMIT",
      "    residues = all(v % 9 in ALLOWED_MOD9 for v in values)",
      "    return cube_sum, height, equation, within_height, residues, equation and within_height",
      "",
      "if len(sys.argv) == 4:",
      "    values = tuple(int(arg, 10) for arg in sys.argv[1:])",
      "    cube_sum, height, equation, within_height, residues, verified = report(*values)",
      "    print(f'x={values[0]} y={values[1]} z={values[2]}')",
      "    print(f'cube_sum={cube_sum} target={TARGET} height={height} limit={HEIGHT_LIMIT}')",
      "    print(f'equation={equation} within_height={within_height} residues_mod9={residues} verified={verified}')",
      "    raise SystemExit(0 if verified else 1)",
      "if len(sys.argv) != 1:",
      "    raise SystemExit('usage: python3 verify.py [X Y Z]')",
      "assert [r for r in range(9) if pow(r, 3, 9) == 8] == [2, 5, 8]",
      "assert report(0, 0, 0) == (0, 0, False, True, False, False)",
      "assert report(2, 5, 8) == (645, 8, False, True, True, False)",
      "print('target=114 height_limit=100000000000000000000')",
      "print('cube_residue_minus_one_mod9=2,5,8')",
      "print('self_tests=2 passed=True')"
    ],
    "missing": [
      "command",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1073/pnas.2022377118",
    "locator": "Inline Python verifier written and executed by TheoremDB entry research on 2026-07-25"
  },
  "relations": [
    {
      "slug": "R769",
      "title": "Every coordinate is 2 modulo 3",
      "object_type": "claim",
      "relation": "evidences",
      "direction": "outgoing"
    },
    {
      "slug": "three-cubes-114-height-1e20",
      "title": "three cubes 114 height 1e20",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}