{
  "status": "PASS",
  "scope": "Exact finite worked examples, not new universal theorems or a Lean run.",
  "counts": {
    "independent_coefficient_equalities": 312,
    "displayed_definitions": 2,
    "normalization_counterexample": 2,
    "odd_prime_sign_control": 3,
    "newton_valuations": 32,
    "newton_exact_reconstruction": 33,
    "newton_precision_256": 33,
    "smooth_tower": 21,
    "singular_no_lift": 3,
    "singular_positive_control": 3,
    "shared_obstruction": 7,
    "weighted_motion": 12
  },
  "total_checks": 463,
  "first_rows": [
    [
      "1",
      "-1",
      "69"
    ],
    [
      "1",
      "-1/5",
      "121/45"
    ],
    [
      "1",
      "-1/15",
      "13/45"
    ],
    [
      "1",
      "-1/35",
      "59/1155"
    ]
  ],
  "normalization": {
    "C1": "-1/84",
    "C2": "703/5460",
    "difference": "64/455",
    "original_difference": "384/455"
  },
  "sign": {
    "C": [
      "1",
      "-1",
      "19"
    ],
    "twisted": [
      "1",
      "1",
      "19"
    ]
  },
  "newton": {
    "first_five": [
      "1",
      "-2",
      "72",
      "-33872",
      "60511872"
    ],
    "mod256": [
      1,
      254,
      72,
      176,
      128
    ],
    "valuations": [
      0,
      1,
      3,
      4,
      7,
      8,
      10,
      11,
      15,
      16,
      18,
      19,
      22,
      23,
      25,
      26,
      31,
      32,
      34,
      35,
      38,
      39,
      41,
      42,
      46,
      47,
      49,
      50,
      53,
      54,
      56,
      57,
      63
    ]
  },
  "tower": [
    {
      "L": 1,
      "modulus": 3,
      "x": 1,
      "residual": -2,
      "digit": 1,
      "next": 4
    },
    {
      "L": 2,
      "modulus": 9,
      "x": 4,
      "residual": 1,
      "digit": 1,
      "next": 13
    },
    {
      "L": 3,
      "modulus": 27,
      "x": 13,
      "residual": 6,
      "digit": 0,
      "next": 13
    },
    {
      "L": 4,
      "modulus": 81,
      "x": 13,
      "residual": 2,
      "digit": 2,
      "next": 175
    },
    {
      "L": 5,
      "modulus": 243,
      "x": 175,
      "residual": 126,
      "digit": 0,
      "next": 175
    },
    {
      "L": 6,
      "modulus": 729,
      "x": 175,
      "residual": 42,
      "digit": 0,
      "next": 175
    },
    {
      "L": 7,
      "modulus": 2187,
      "x": 175,
      "residual": 14,
      "digit": 2,
      "next": 4549
    }
  ],
  "blocked_residues": [
    6,
    6,
    6
  ],
  "shared_residuals": [
    [
      0,
      2
    ],
    [
      1,
      0
    ],
    [
      2,
      1
    ]
  ],
  "motion": [
    {
      "A": 2,
      "root": -3,
      "coefficient_valuation": 2,
      "motion_valuation": 1
    },
    {
      "A": 3,
      "root": -9,
      "coefficient_valuation": 3,
      "motion_valuation": 2
    },
    {
      "A": 4,
      "root": -27,
      "coefficient_valuation": 4,
      "motion_valuation": 3
    },
    {
      "A": 5,
      "root": -81,
      "coefficient_valuation": 5,
      "motion_valuation": 4
    },
    {
      "A": 6,
      "root": -243,
      "coefficient_valuation": 6,
      "motion_valuation": 5
    },
    {
      "A": 7,
      "root": -729,
      "coefficient_valuation": 7,
      "motion_valuation": 6
    }
  ]
}