{
  "generated_at_utc": "2026-10-09T00:56:16.255149+00:00",
  "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
  "runtime": {
    "interpreter": "/opt/homebrew/opt/python@3.10/bin/python3.10",
    "python": "3.10.19",
    "sympy": "1.13.1",
    "platform": "macOS-27.2-arm64-arm-64bit"
  },
  "source_files": [
    {
      "path": "lean/docs/116.md",
      "sha256": "c3b9d25576399946bc0bdb9f63cb8cb1a7f30161edb2319f120911fded2c8a63"
    },
    {
      "path": "lean/ComparatorChallenges/FormulaHitting.lean",
      "sha256": "23f279f5ed50b1a8a86df490c0157866e120a279b552489f1ae180e7dd3f01bd"
    },
    {
      "path": "lean/ComparatorChallenges/FormulaHitting.json",
      "sha256": "a992f877ec771761914d814aefee436f030b634e811911965ade14b2112e0b2a"
    },
    {
      "path": "lean/OAI/Algebra/FormulaHitting/Hitting.lean",
      "sha256": "7d5388765abe1cb35041801422b96f55648805b3dd87da28c29a44b7301dcd30"
    },
    {
      "path": "lean/ComparatorChallenges/RationalHitting.lean",
      "sha256": "c0fc0d9740d4ef195918447f4da9605e75760845cae1163c534d6299c6e4877f"
    },
    {
      "path": "lean/ComparatorChallenges/RationalHitting.json",
      "sha256": "2b135eaf875cd6c699fd8dd9b9b8073f11da8ef767c581fd2e1b65d15d250dee"
    },
    {
      "path": "lean/OAI/Computability/RationalHitting/Main.lean",
      "sha256": "1de92103466695d67f6bbdbf44690af033aab4fb7e232228a702d3434e5203cd"
    },
    {
      "path": "preprints/Uniform-Matrix-Hitting-Points-in-Every-Positive-Characteristic-October-4-2026/uniform-matrix-hitting-points-positive-characteristic.pdf",
      "sha256": "06284554d3db1df4569dff00d12df083815bf1bafc401f9c97f4ba9cc09119fc"
    },
    {
      "path": "preprints/One-Rational-Matrix-Hitting-Point-for-Noncommutative-Formulas-September-24-2026/One-Rational-Matrix-Hitting-Point-for-Noncommutative-Formulas-September-24-2026.pdf",
      "sha256": "984d0d4287bc29fc4772a2254aabafb9ee8886c56eeafeef0a746c7fc06869ed"
    },
    {
      "path": "preprints/Polynomial-Hitting-Lists-for-Noncommutative-Rational-Formulas-September-24-2026/Polynomial-Hitting-Lists-for-Noncommutative-Rational-Formulas-September-24-2026.pdf",
      "sha256": "8f6fe5057bd59278bfb88ccf38342c09602e547f35a757b8eadc30ece76cec0e"
    }
  ],
  "tiny_formula_count": 548,
  "tiny_controls": [
    {
      "number": 0,
      "gates": 1,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 1,
      "gates": 1,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 2,
      "gates": 1,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 3,
      "gates": 1,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 4,
      "gates": 3,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 5,
      "gates": 3,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 6,
      "gates": 3,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 7,
      "gates": 3,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 8,
      "gates": 3,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 9,
      "gates": 3,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 10,
      "gates": 3,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 11,
      "gates": 3,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 12,
      "gates": 3,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 13,
      "gates": 3,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 14,
      "gates": 3,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 15,
      "gates": 3,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 16,
      "gates": 3,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 17,
      "gates": 3,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 18,
      "gates": 3,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 19,
      "gates": 3,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 20,
      "gates": 3,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 21,
      "gates": 3,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 22,
      "gates": 3,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 23,
      "gates": 3,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 24,
      "gates": 3,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 25,
      "gates": 3,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 26,
      "gates": 3,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 27,
      "gates": 3,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 28,
      "gates": 3,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 29,
      "gates": 3,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 30,
      "gates": 3,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 31,
      "gates": 3,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 32,
      "gates": 3,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 33,
      "gates": 3,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 34,
      "gates": 3,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 35,
      "gates": 3,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 36,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 37,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 38,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 39,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 40,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 41,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 42,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 43,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 44,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 45,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 46,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 47,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 48,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 49,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 50,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 51,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 52,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 53,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 54,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 55,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 56,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 57,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 58,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 59,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 60,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 61,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 62,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 63,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 64,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 65,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 66,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 67,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 68,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 69,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 70,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 71,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 72,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 73,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 74,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 75,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 76,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 77,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 78,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 79,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 80,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 81,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 82,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 83,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 84,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 85,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 86,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 87,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 88,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 89,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 90,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 91,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 92,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 93,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 94,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 95,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 96,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 97,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 98,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 99,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 100,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 101,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 102,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 103,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 104,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 105,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 106,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 107,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 108,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 109,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 110,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 111,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 112,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 113,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 114,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 115,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 116,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 117,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 118,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 119,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 120,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 121,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 122,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 123,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 124,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 125,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 126,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 127,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 128,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 129,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 130,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 131,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 132,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 133,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 134,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 135,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 136,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 137,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 138,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 139,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 140,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 141,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 142,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 143,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 144,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 145,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 146,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 147,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 148,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 149,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 150,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 151,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 152,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 153,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 154,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 155,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 156,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 157,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 158,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 159,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 160,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 161,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 162,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 163,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 164,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 165,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 166,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 167,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 168,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 169,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 170,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 171,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 172,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 173,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 174,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 175,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 176,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 177,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 178,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 179,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 180,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 181,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 182,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 183,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 184,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 185,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 186,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 187,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 188,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 189,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 190,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 191,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 192,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 193,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 194,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 195,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 196,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 197,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 198,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 199,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 200,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 201,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 202,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 203,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 204,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 205,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 206,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 207,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 208,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 209,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 210,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 211,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 212,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 213,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 214,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 215,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 216,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 217,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 218,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 219,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 220,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 221,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 222,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 223,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 224,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 225,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 226,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 227,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 228,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 229,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 230,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 231,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 232,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 233,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 234,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 235,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 236,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 237,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 238,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 239,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 240,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 241,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 242,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 243,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 244,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 245,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 246,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 247,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 248,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 249,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 250,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 251,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 252,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 253,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 254,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 255,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 256,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 257,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 258,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 259,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 260,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 261,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 262,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 263,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 264,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 265,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 266,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 267,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 268,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 269,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 270,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 271,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 272,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 273,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 274,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 275,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 276,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 277,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 278,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 279,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 280,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 281,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 282,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 283,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 284,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 285,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 286,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 287,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 288,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 289,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 290,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 291,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 292,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 293,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 294,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 295,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 296,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 297,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 298,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 299,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 300,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 301,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 302,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 303,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 304,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 305,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 306,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 307,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 308,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 309,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 310,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 311,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 312,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 313,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 314,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 315,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 316,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 317,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 318,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 319,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 320,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 321,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 322,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 323,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 324,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 325,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 326,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 327,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 328,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 329,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 330,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 331,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 332,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 333,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 334,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 335,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 336,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 337,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 338,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 339,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 340,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 341,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 342,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 343,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 344,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 345,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 346,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 347,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 348,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 349,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 350,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 351,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 352,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 353,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 354,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 355,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 356,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 357,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 358,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 359,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 360,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 361,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 362,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 363,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 364,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 365,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 366,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 367,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 368,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 369,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 370,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 371,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 372,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 373,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 374,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 375,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 376,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 377,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 378,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 379,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 380,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 381,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 382,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 383,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 384,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 385,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 386,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 387,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 388,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 389,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 390,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 391,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 392,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 393,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 394,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 395,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 396,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 397,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 398,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 399,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 400,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 401,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 402,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 403,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 404,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 405,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 406,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 407,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 408,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 409,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 410,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 411,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 412,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 413,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 414,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 415,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 416,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 417,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 418,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 419,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 420,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 421,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 422,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 423,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 424,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 425,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 426,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 427,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 428,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 429,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 430,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 431,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 432,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 433,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 434,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 435,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 436,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 437,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 438,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 439,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 440,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 441,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 442,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 443,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 444,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 445,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 446,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 447,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 448,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 449,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 450,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 451,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 452,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 453,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 454,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 455,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 456,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 457,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 458,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 459,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 460,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 461,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 462,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 463,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 464,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 465,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 466,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 467,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 468,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 469,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 470,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 471,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 472,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 473,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 474,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 475,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 476,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 477,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 478,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 479,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 480,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 481,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 482,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 483,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 484,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 485,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 486,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 487,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 488,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 489,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 490,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 491,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 492,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 493,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 494,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 495,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 496,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 497,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 498,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 499,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 500,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 501,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 502,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 503,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 504,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 505,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 506,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 507,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 508,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 509,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 510,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 511,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 512,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 513,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 514,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 515,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 516,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 517,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 518,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 519,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 520,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 521,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 522,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 523,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 524,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 525,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 526,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 527,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 528,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 529,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 530,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 531,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 532,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 533,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 534,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 535,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 536,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 537,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 538,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 539,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 540,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 541,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 542,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 543,
      "gates": 5,
      "nonzero": false,
      "status": "zero_at_source_tuple_conditional"
    },
    {
      "number": 544,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 545,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 546,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    },
    {
      "number": 547,
      "gates": 5,
      "nonzero": true,
      "status": "nonzero_polynomial_witness"
    }
  ],
  "cases": [
    {
      "case": "ordered_commutator",
      "reference": {
        "variables": 2,
        "gates": 9,
        "source_dimension": 324,
        "requested_dimension": 324,
        "completed_dimension": 324,
        "requested_full_source_dimension": true,
        "model": {
          "field": "rational_characteristic_zero",
          "algebra": "free_associative",
          "gates": "division_free_tree"
        },
        "independent_identity_conclusion": "not_an_identity_in_the_declared_free_rational_algebra",
        "source_universal_hitting_acceptance": "not_independently_verified",
        "implementation": "Visible formula tree; structured rational matrix action, not an opaque black-box oracle",
        "budget_scope": "Counts selected rational add/multiply/divide calls only; excludes parsing, negation, bit arithmetic, allocation and wall time",
        "status": "nonzero_polynomial_witness",
        "witness": {
          "row": 3,
          "column": 0,
          "value": "-1/24",
          "dimension": 324,
          "generator": "[1] for n=s=1; otherwise entry (-1)^(r-q-1)/(r*i^(r-q)) for q<r, zero otherwise"
        },
        "arithmetic_charges": 4524
      },
      "prefix_32": {
        "variables": 2,
        "gates": 9,
        "source_dimension": 324,
        "requested_dimension": 32,
        "completed_dimension": 32,
        "requested_full_source_dimension": false,
        "model": {
          "field": "rational_characteristic_zero",
          "algebra": "free_associative",
          "gates": "division_free_tree"
        },
        "independent_identity_conclusion": "not_an_identity_in_the_declared_free_rational_algebra",
        "source_universal_hitting_acceptance": "not_independently_verified",
        "implementation": "Visible formula tree; structured rational matrix action, not an opaque black-box oracle",
        "budget_scope": "Counts selected rational add/multiply/divide calls only; excludes parsing, negation, bit arithmetic, allocation and wall time",
        "status": "nonzero_polynomial_witness",
        "witness": {
          "row": 3,
          "column": 0,
          "value": "-1/24",
          "dimension": 32,
          "generator": "[1] for n=s=1; otherwise entry (-1)^(r-q-1)/(r*i^(r-q)) for q<r, zero otherwise"
        },
        "arithmetic_charges": 436
      },
      "reference_ns": 5183250,
      "prefix_32_ns": 419666,
      "sympy_ns": 122458,
      "sympy_terms": 2,
      "sympy_identity": false,
      "input": {
        "path": "ordered_commutator-input.json",
        "sha256": "d2712ce6f9719eb423258aabdc5bd186d0f31721ce1809a8382e25cc8076b55f"
      }
    },
    {
      "case": "distributive_identity",
      "reference": {
        "variables": 3,
        "gates": 15,
        "source_dimension": 1350,
        "requested_dimension": 1350,
        "completed_dimension": 1350,
        "requested_full_source_dimension": true,
        "model": {
          "field": "rational_characteristic_zero",
          "algebra": "free_associative",
          "gates": "division_free_tree"
        },
        "independent_identity_conclusion": "unknown",
        "source_universal_hitting_acceptance": "not_independently_verified",
        "implementation": "Visible formula tree; structured rational matrix action, not an opaque black-box oracle",
        "budget_scope": "Counts selected rational add/multiply/divide calls only; excludes parsing, negation, bit arithmetic, allocation and wall time",
        "status": "zero_at_source_tuple_conditional",
        "conditional_interpretation": "A full-dimension zero first column implies identity only under the source paper detection argument and correct implementation; neither is formally accepted here",
        "arithmetic_charges": 33729
      },
      "prefix_32": {
        "variables": 3,
        "gates": 15,
        "source_dimension": 1350,
        "requested_dimension": 32,
        "completed_dimension": 32,
        "requested_full_source_dimension": false,
        "model": {
          "field": "rational_characteristic_zero",
          "algebra": "free_associative",
          "gates": "division_free_tree"
        },
        "independent_identity_conclusion": "unknown",
        "source_universal_hitting_acceptance": "not_independently_verified",
        "implementation": "Visible formula tree; structured rational matrix action, not an opaque black-box oracle",
        "budget_scope": "Counts selected rational add/multiply/divide calls only; excludes parsing, negation, bit arithmetic, allocation and wall time",
        "status": "zero_at_truncation_unknown",
        "conditional_interpretation": "A full-dimension zero first column implies identity only under the source paper detection argument and correct implementation; neither is formally accepted here",
        "arithmetic_charges": 779
      },
      "reference_ns": 111394333,
      "prefix_32_ns": 795500,
      "sympy_ns": 365250,
      "sympy_terms": 0,
      "sympy_identity": true,
      "input": {
        "path": "distributive_identity-input.json",
        "sha256": "7c004fed61b7ae7dae7eea12c7ea940269cfa3ffcd0e1d1496495e2dd4ef4c35"
      }
    },
    {
      "case": "incorrect_square_rewrite",
      "reference": {
        "variables": 2,
        "gates": 23,
        "source_dimension": 2116,
        "requested_dimension": 2116,
        "completed_dimension": 2116,
        "requested_full_source_dimension": true,
        "model": {
          "field": "rational_characteristic_zero",
          "algebra": "free_associative",
          "gates": "division_free_tree"
        },
        "independent_identity_conclusion": "not_an_identity_in_the_declared_free_rational_algebra",
        "source_universal_hitting_acceptance": "not_independently_verified",
        "implementation": "Visible formula tree; structured rational matrix action, not an opaque black-box oracle",
        "budget_scope": "Counts selected rational add/multiply/divide calls only; excludes parsing, negation, bit arithmetic, allocation and wall time",
        "status": "nonzero_polynomial_witness",
        "witness": {
          "row": 3,
          "column": 0,
          "value": "1/24",
          "dimension": 2116,
          "generator": "[1] for n=s=1; otherwise entry (-1)^(r-q-1)/(r*i^(r-q)) for q<r, zero otherwise"
        },
        "arithmetic_charges": 78262
      },
      "prefix_32": {
        "variables": 2,
        "gates": 23,
        "source_dimension": 2116,
        "requested_dimension": 32,
        "completed_dimension": 32,
        "requested_full_source_dimension": false,
        "model": {
          "field": "rational_characteristic_zero",
          "algebra": "free_associative",
          "gates": "division_free_tree"
        },
        "independent_identity_conclusion": "not_an_identity_in_the_declared_free_rational_algebra",
        "source_universal_hitting_acceptance": "not_independently_verified",
        "implementation": "Visible formula tree; structured rational matrix action, not an opaque black-box oracle",
        "budget_scope": "Counts selected rational add/multiply/divide calls only; excludes parsing, negation, bit arithmetic, allocation and wall time",
        "status": "nonzero_polynomial_witness",
        "witness": {
          "row": 3,
          "column": 0,
          "value": "1/24",
          "dimension": 32,
          "generator": "[1] for n=s=1; otherwise entry (-1)^(r-q-1)/(r*i^(r-q)) for q<r, zero otherwise"
        },
        "arithmetic_charges": 1154
      },
      "reference_ns": 313175750,
      "prefix_32_ns": 1120250,
      "sympy_ns": 473792,
      "sympy_terms": 2,
      "sympy_identity": false,
      "input": {
        "path": "incorrect_square_rewrite-input.json",
        "sha256": "6cd23f78162e07fc7a92a5adb5e9285dfa3e42cb8389691343796a77ad0e521e"
      }
    },
    {
      "case": "rational_scalar",
      "reference": {
        "variables": 2,
        "gates": 5,
        "source_dimension": 100,
        "requested_dimension": 100,
        "completed_dimension": 100,
        "requested_full_source_dimension": true,
        "model": {
          "field": "rational_characteristic_zero",
          "algebra": "free_associative",
          "gates": "division_free_tree"
        },
        "independent_identity_conclusion": "not_an_identity_in_the_declared_free_rational_algebra",
        "source_universal_hitting_acceptance": "not_independently_verified",
        "implementation": "Visible formula tree; structured rational matrix action, not an opaque black-box oracle",
        "budget_scope": "Counts selected rational add/multiply/divide calls only; excludes parsing, negation, bit arithmetic, allocation and wall time",
        "status": "nonzero_polynomial_witness",
        "witness": {
          "row": 0,
          "column": 0,
          "value": "2/3",
          "dimension": 100,
          "generator": "[1] for n=s=1; otherwise entry (-1)^(r-q-1)/(r*i^(r-q)) for q<r, zero otherwise"
        },
        "arithmetic_charges": 597
      },
      "prefix_32": {
        "variables": 2,
        "gates": 5,
        "source_dimension": 100,
        "requested_dimension": 32,
        "completed_dimension": 32,
        "requested_full_source_dimension": false,
        "model": {
          "field": "rational_characteristic_zero",
          "algebra": "free_associative",
          "gates": "division_free_tree"
        },
        "independent_identity_conclusion": "not_an_identity_in_the_declared_free_rational_algebra",
        "source_universal_hitting_acceptance": "not_independently_verified",
        "implementation": "Visible formula tree; structured rational matrix action, not an opaque black-box oracle",
        "budget_scope": "Counts selected rational add/multiply/divide calls only; excludes parsing, negation, bit arithmetic, allocation and wall time",
        "status": "nonzero_polynomial_witness",
        "witness": {
          "row": 0,
          "column": 0,
          "value": "2/3",
          "dimension": 32,
          "generator": "[1] for n=s=1; otherwise entry (-1)^(r-q-1)/(r*i^(r-q)) for q<r, zero otherwise"
        },
        "arithmetic_charges": 189
      },
      "reference_ns": 542250,
      "prefix_32_ns": 170917,
      "sympy_ns": 239209,
      "sympy_terms": 2,
      "sympy_identity": false,
      "input": {
        "path": "rational_scalar-input.json",
        "sha256": "b1ef26636c22af0eb04e4aa5e951ec1e2b7203994832f1ae3f385c8793568d96"
      }
    },
    {
      "case": "exceptional_variable",
      "reference": {
        "variables": 1,
        "gates": 1,
        "source_dimension": 1,
        "requested_dimension": 1,
        "completed_dimension": 1,
        "requested_full_source_dimension": true,
        "model": {
          "field": "rational_characteristic_zero",
          "algebra": "free_associative",
          "gates": "division_free_tree"
        },
        "independent_identity_conclusion": "not_an_identity_in_the_declared_free_rational_algebra",
        "source_universal_hitting_acceptance": "not_independently_verified",
        "implementation": "Visible formula tree; structured rational matrix action, not an opaque black-box oracle",
        "budget_scope": "Counts selected rational add/multiply/divide calls only; excludes parsing, negation, bit arithmetic, allocation and wall time",
        "status": "nonzero_polynomial_witness",
        "witness": {
          "row": 0,
          "column": 0,
          "value": "1",
          "dimension": 1,
          "generator": "[1] for n=s=1; otherwise entry (-1)^(r-q-1)/(r*i^(r-q)) for q<r, zero otherwise"
        },
        "arithmetic_charges": 0
      },
      "prefix_32": {
        "variables": 1,
        "gates": 1,
        "source_dimension": 1,
        "requested_dimension": 1,
        "completed_dimension": 1,
        "requested_full_source_dimension": true,
        "model": {
          "field": "rational_characteristic_zero",
          "algebra": "free_associative",
          "gates": "division_free_tree"
        },
        "independent_identity_conclusion": "not_an_identity_in_the_declared_free_rational_algebra",
        "source_universal_hitting_acceptance": "not_independently_verified",
        "implementation": "Visible formula tree; structured rational matrix action, not an opaque black-box oracle",
        "budget_scope": "Counts selected rational add/multiply/divide calls only; excludes parsing, negation, bit arithmetic, allocation and wall time",
        "status": "nonzero_polynomial_witness",
        "witness": {
          "row": 0,
          "column": 0,
          "value": "1",
          "dimension": 1,
          "generator": "[1] for n=s=1; otherwise entry (-1)^(r-q-1)/(r*i^(r-q)) for q<r, zero otherwise"
        },
        "arithmetic_charges": 0
      },
      "reference_ns": 10292,
      "prefix_32_ns": 3250,
      "sympy_ns": 3750,
      "sympy_terms": 1,
      "sympy_identity": false,
      "input": {
        "path": "exceptional_variable-input.json",
        "sha256": "41496b40ea790574ab1a446a81153d8367502c99a9ca6c1e7858ef395eed8739"
      }
    },
    {
      "case": "product_of_sums_2",
      "reference": {
        "variables": 2,
        "gates": 7,
        "source_dimension": 196,
        "requested_dimension": 196,
        "completed_dimension": 196,
        "requested_full_source_dimension": true,
        "model": {
          "field": "rational_characteristic_zero",
          "algebra": "free_associative",
          "gates": "division_free_tree"
        },
        "independent_identity_conclusion": "not_an_identity_in_the_declared_free_rational_algebra",
        "source_universal_hitting_acceptance": "not_independently_verified",
        "implementation": "Visible formula tree; structured rational matrix action, not an opaque black-box oracle",
        "budget_scope": "Counts selected rational add/multiply/divide calls only; excludes parsing, negation, bit arithmetic, allocation and wall time",
        "status": "nonzero_polynomial_witness",
        "witness": {
          "row": 2,
          "column": 0,
          "value": "9/8",
          "dimension": 196,
          "generator": "[1] for n=s=1; otherwise entry (-1)^(r-q-1)/(r*i^(r-q)) for q<r, zero otherwise"
        },
        "arithmetic_charges": 2732
      },
      "prefix_32": {
        "variables": 2,
        "gates": 7,
        "source_dimension": 196,
        "requested_dimension": 32,
        "completed_dimension": 32,
        "requested_full_source_dimension": false,
        "model": {
          "field": "rational_characteristic_zero",
          "algebra": "free_associative",
          "gates": "division_free_tree"
        },
        "independent_identity_conclusion": "not_an_identity_in_the_declared_free_rational_algebra",
        "source_universal_hitting_acceptance": "not_independently_verified",
        "implementation": "Visible formula tree; structured rational matrix action, not an opaque black-box oracle",
        "budget_scope": "Counts selected rational add/multiply/divide calls only; excludes parsing, negation, bit arithmetic, allocation and wall time",
        "status": "nonzero_polynomial_witness",
        "witness": {
          "row": 2,
          "column": 0,
          "value": "9/8",
          "dimension": 32,
          "generator": "[1] for n=s=1; otherwise entry (-1)^(r-q-1)/(r*i^(r-q)) for q<r, zero otherwise"
        },
        "arithmetic_charges": 436
      },
      "reference_ns": 3066542,
      "prefix_32_ns": 428834,
      "sympy_ns": 85667,
      "sympy_terms": 4,
      "sympy_identity": false,
      "input": {
        "path": "product_of_sums_2-input.json",
        "sha256": "b7933dd1a4a67850373654a2adfd787647597dd0b054f21e5117e7b57e1ede1f"
      }
    },
    {
      "case": "product_of_sums_4",
      "reference": {
        "variables": 2,
        "gates": 15,
        "source_dimension": 900,
        "requested_dimension": 900,
        "completed_dimension": 900,
        "requested_full_source_dimension": true,
        "model": {
          "field": "rational_characteristic_zero",
          "algebra": "free_associative",
          "gates": "division_free_tree"
        },
        "independent_identity_conclusion": "not_an_identity_in_the_declared_free_rational_algebra",
        "source_universal_hitting_acceptance": "not_independently_verified",
        "implementation": "Visible formula tree; structured rational matrix action, not an opaque black-box oracle",
        "budget_scope": "Counts selected rational add/multiply/divide calls only; excludes parsing, negation, bit arithmetic, allocation and wall time",
        "status": "nonzero_polynomial_witness",
        "witness": {
          "row": 4,
          "column": 0,
          "value": "27/128",
          "dimension": 900,
          "generator": "[1] for n=s=1; otherwise entry (-1)^(r-q-1)/(r*i^(r-q)) for q<r, zero otherwise"
        },
        "arithmetic_charges": 25176
      },
      "prefix_32": {
        "variables": 2,
        "gates": 15,
        "source_dimension": 900,
        "requested_dimension": 32,
        "completed_dimension": 32,
        "requested_full_source_dimension": false,
        "model": {
          "field": "rational_characteristic_zero",
          "algebra": "free_associative",
          "gates": "division_free_tree"
        },
        "independent_identity_conclusion": "not_an_identity_in_the_declared_free_rational_algebra",
        "source_universal_hitting_acceptance": "not_independently_verified",
        "implementation": "Visible formula tree; structured rational matrix action, not an opaque black-box oracle",
        "budget_scope": "Counts selected rational add/multiply/divide calls only; excludes parsing, negation, bit arithmetic, allocation and wall time",
        "status": "nonzero_polynomial_witness",
        "witness": {
          "row": 4,
          "column": 0,
          "value": "27/128",
          "dimension": 32,
          "generator": "[1] for n=s=1; otherwise entry (-1)^(r-q-1)/(r*i^(r-q)) for q<r, zero otherwise"
        },
        "arithmetic_charges": 872
      },
      "reference_ns": 83534459,
      "prefix_32_ns": 856792,
      "sympy_ns": 1119333,
      "sympy_terms": 16,
      "sympy_identity": false,
      "input": {
        "path": "product_of_sums_4-input.json",
        "sha256": "e1f0bf003398bee1455c23bc8d0e1e3e6ae714d860d1d1b8605152c99678feb0"
      }
    },
    {
      "case": "product_of_sums_8",
      "reference": {
        "variables": 2,
        "gates": 31,
        "source_dimension": 3844,
        "requested_dimension": 3844,
        "completed_dimension": null,
        "requested_full_source_dimension": true,
        "model": {
          "field": "rational_characteristic_zero",
          "algebra": "free_associative",
          "gates": "division_free_tree"
        },
        "independent_identity_conclusion": "unknown",
        "source_universal_hitting_acceptance": "not_independently_verified",
        "implementation": "Visible formula tree; structured rational matrix action, not an opaque black-box oracle",
        "budget_scope": "Counts selected rational add/multiply/divide calls only; excludes parsing, negation, bit arithmetic, allocation and wall time",
        "status": "unknown",
        "reason": "intermediate rational bit cap exceeded",
        "arithmetic_charges": 36985
      },
      "prefix_32": {
        "variables": 2,
        "gates": 31,
        "source_dimension": 3844,
        "requested_dimension": 32,
        "completed_dimension": 32,
        "requested_full_source_dimension": false,
        "model": {
          "field": "rational_characteristic_zero",
          "algebra": "free_associative",
          "gates": "division_free_tree"
        },
        "independent_identity_conclusion": "not_an_identity_in_the_declared_free_rational_algebra",
        "source_universal_hitting_acceptance": "not_independently_verified",
        "implementation": "Visible formula tree; structured rational matrix action, not an opaque black-box oracle",
        "budget_scope": "Counts selected rational add/multiply/divide calls only; excludes parsing, negation, bit arithmetic, allocation and wall time",
        "status": "nonzero_polynomial_witness",
        "witness": {
          "row": 8,
          "column": 0,
          "value": "729/1146880",
          "dimension": 32,
          "generator": "[1] for n=s=1; otherwise entry (-1)^(r-q-1)/(r*i^(r-q)) for q<r, zero otherwise"
        },
        "arithmetic_charges": 1744
      },
      "reference_ns": 136787042,
      "prefix_32_ns": 1771041,
      "sympy_ns": 27911666,
      "sympy_terms": 256,
      "sympy_identity": false,
      "input": {
        "path": "product_of_sums_8-input.json",
        "sha256": "bd07c413bdad2f034df62065d324f1df7e5b16b0de38a1ae80f03b492e1c7d90"
      }
    },
    {
      "case": "product_of_sums_16",
      "reference": {
        "variables": 2,
        "gates": 63,
        "source_dimension": 15876,
        "requested_dimension": 15876,
        "completed_dimension": null,
        "requested_full_source_dimension": true,
        "model": {
          "field": "rational_characteristic_zero",
          "algebra": "free_associative",
          "gates": "division_free_tree"
        },
        "independent_identity_conclusion": "unknown",
        "source_universal_hitting_acceptance": "not_independently_verified",
        "implementation": "Visible formula tree; structured rational matrix action, not an opaque black-box oracle",
        "budget_scope": "Counts selected rational add/multiply/divide calls only; excludes parsing, negation, bit arithmetic, allocation and wall time",
        "status": "unknown",
        "reason": "intermediate rational bit cap exceeded",
        "arithmetic_charges": 72165
      },
      "prefix_32": {
        "variables": 2,
        "gates": 63,
        "source_dimension": 15876,
        "requested_dimension": 32,
        "completed_dimension": 32,
        "requested_full_source_dimension": false,
        "model": {
          "field": "rational_characteristic_zero",
          "algebra": "free_associative",
          "gates": "division_free_tree"
        },
        "independent_identity_conclusion": "not_an_identity_in_the_declared_free_rational_algebra",
        "source_universal_hitting_acceptance": "not_independently_verified",
        "implementation": "Visible formula tree; structured rational matrix action, not an opaque black-box oracle",
        "budget_scope": "Counts selected rational add/multiply/divide calls only; excludes parsing, negation, bit arithmetic, allocation and wall time",
        "status": "nonzero_polynomial_witness",
        "witness": {
          "row": 16,
          "column": 0,
          "value": "59049/1880927240192000",
          "dimension": 32,
          "generator": "[1] for n=s=1; otherwise entry (-1)^(r-q-1)/(r*i^(r-q)) for q<r, zero otherwise"
        },
        "arithmetic_charges": 3488
      },
      "reference_ns": 71941542,
      "prefix_32_ns": 3523625,
      "sympy_ns": 14772280292,
      "sympy_terms": 65536,
      "sympy_identity": false,
      "input": {
        "path": "product_of_sums_16-input.json",
        "sha256": "b582921813da38bba5a4395e75609836042952d60692414bc56673e745cd1e4e"
      }
    }
  ],
  "source_schedules": [
    {
      "n": 1,
      "s": 1,
      "polynomial_dimension": 1,
      "polynomial_dense_entries": 1,
      "positive_characteristic_N": 2,
      "positive_characteristic_E": 3,
      "positive_characteristic_dimension": 6,
      "positive_characteristic_dense_entries": 36,
      "rational_B": 3,
      "rational_delta": 48,
      "rational_M": 256,
      "rational_dimension": 32768,
      "rational_H": 452984833,
      "rational_grid_triples": 92950340097909002166337537
    },
    {
      "n": 2,
      "s": 3,
      "polynomial_dimension": 36,
      "polynomial_dense_entries": 2592,
      "positive_characteristic_N": 31,
      "positive_characteristic_E": 526,
      "positive_characteristic_dimension": 16306,
      "positive_characteristic_dense_entries": 531771272,
      "rational_B": 7,
      "rational_delta": 378,
      "rational_M": 4096,
      "rational_dimension": 8388608,
      "rational_H": 7215545057281,
      "rational_grid_triples": 375670790678992431863771923481666519041
    },
    {
      "n": 2,
      "s": 9,
      "polynomial_dimension": 324,
      "polynomial_dense_entries": 209952,
      "positive_characteristic_N": 307,
      "positive_characteristic_E": 47584,
      "positive_characteristic_dimension": 14608288,
      "positive_characteristic_dense_entries": 426804156581888,
      "rational_B": 19,
      "rational_delta": 1026,
      "rational_M": 32768,
      "rational_dimension": 536870912,
      "rational_H": 22060601299697665,
      "rational_grid_triples": 10736235695876997810245769403257872033307766554625
    },
    {
      "n": 2,
      "s": 31,
      "polynomial_dimension": 3844,
      "polynomial_dense_entries": 29552672,
      "positive_characteristic_N": 3783,
      "positive_characteristic_E": 7161218,
      "positive_characteristic_dimension": 27090887694,
      "positive_characteristic_dense_entries": 1467832392097841275272,
      "rational_B": 63,
      "rational_delta": 3402,
      "rational_M": 262144,
      "rational_dimension": 34359738368,
      "rational_H": 112355803503639134209,
      "rational_grid_triples": 1418360178793051471768867131274247759546579101346749457891329
    },
    {
      "n": 4,
      "s": 63,
      "polynomial_dimension": 31752,
      "polynomial_dense_entries": 4032758016,
      "positive_characteristic_N": 31501,
      "positive_characteristic_E": 496266751,
      "positive_characteristic_dimension": 15632898923251,
      "positive_characteristic_dense_entries": 977550114978329100753636004,
      "rational_B": 127,
      "rational_delta": 31750,
      "rational_M": 4194304,
      "rational_dimension": 8796093022208,
      "rational_H": 1827334467941668183080961,
      "rational_grid_triples": 6101746186916524883221652220201965008844081068201712555498398010761543681
    },
    {
      "n": 8,
      "s": 127,
      "polynomial_dimension": 258064,
      "polynomial_dense_entries": 532776224768,
      "positive_characteristic_N": 257049,
      "positive_characteristic_E": 33039022061,
      "positive_characteristic_dimension": 8492647581757989,
      "positive_characteristic_dense_entries": 577000503583518547648990122592968,
      "rational_B": 255,
      "rational_delta": 371790,
      "rational_M": 134217728,
      "rational_dimension": 9007199254740992,
      "rational_H": 238605689017339360211757957121,
      "rational_grid_triples": 13584460105755699884646190896080844286105505319778108456562136067544260048198964934082561
    }
  ],
  "interpretation": "Exact rational finite witnesses and independent finite controls; source universal proof remains unaccepted. Visible-tree implementation, no black-box API or overall speedup claim. Timings are one sequential local sample per method."
}
