{
  "finite_observation": {
    "cases": 108,
    "sample_certificates": [
      {
        "p": 2,
        "q": 3,
        "M": 12,
        "k": 2,
        "L": 2,
        "modular_state": 4,
        "selected_powers": [
          4,
          16,
          64
        ],
        "target_values": [
          9,
          81,
          729
        ],
        "sharp_error": "36",
        "witness_lambda": "12",
        "witness_kappa": "-75"
      },
      {
        "p": 2,
        "q": 3,
        "M": 360,
        "k": 3,
        "L": 12,
        "modular_state": 8,
        "selected_powers": [
          8,
          32768,
          134217728
        ],
        "target_values": [
          27,
          14348907,
          7625597484987
        ],
        "sharp_error": "3783405061800/4097",
        "witness_lambda": "232771596/4097",
        "witness_kappa": "-923911917"
      },
      {
        "p": 3,
        "q": 5,
        "M": 27,
        "k": 3,
        "L": 1,
        "modular_state": 0,
        "selected_powers": [
          27,
          81,
          243
        ],
        "target_values": [
          125,
          625,
          3125
        ],
        "sharp_error": "125",
        "witness_lambda": "125/9",
        "witness_kappa": "-375"
      }
    ],
    "max_period": 332,
    "pass": true
  },
  "polyphase": {
    "cases": 420,
    "sample_certificates": [
      {
        "p": 2,
        "q": 3,
        "s": 1,
        "d": 0,
        "k": 1,
        "sharp_error": "1",
        "numerator": 6,
        "filter_coefficients": [
          2,
          -3,
          1
        ],
        "witness_coefficients": [
          "4",
          "-6"
        ]
      },
      {
        "p": 2,
        "q": 3,
        "s": 2,
        "d": 1,
        "k": 1,
        "sharp_error": "48",
        "numerator": 960,
        "filter_coefficients": [
          -4,
          9,
          -6,
          1
        ],
        "witness_coefficients": [
          "64/3",
          "25/3",
          "-200"
        ]
      },
      {
        "p": 3,
        "q": 5,
        "s": 2,
        "d": 2,
        "k": 2,
        "sharp_error": "69120",
        "numerator": 5529600,
        "filter_coefficients": [
          9,
          -28,
          30,
          -12,
          1
        ],
        "witness_coefficients": [
          "195",
          "-70850",
          "312000",
          "-187200"
        ]
      }
    ],
    "pass": true
  },
  "witt": {
    "cases": 45,
    "lift_pairs": 31398,
    "cocycle_triples": 12093,
    "nontrivial_cycle_each": true,
    "pass": true,
    "sample": [
      {
        "p": 2,
        "N": 2,
        "cycle": 1,
        "pairs": 4,
        "triples": 8
      },
      {
        "p": 3,
        "N": 2,
        "cycle": 1,
        "pairs": 9,
        "triples": 27
      },
      {
        "p": 5,
        "N": 3,
        "cycle": 1,
        "pairs": 25,
        "triples": 125
      },
      {
        "p": 11,
        "N": 4,
        "cycle": 1,
        "pairs": 121,
        "triples": 1331
      }
    ]
  },
  "boundary_tests": {
    "no_additive_split_mod_p_squared": 328,
    "explicit_p3_carry_1_plus_1": 1,
    "note": "classical nonsplit additive extension; no abc-height claim"
  }
}