{
  "status": "PASS",
  "checks": 45440,
  "groups": {
    "extra_y4_relation": 1,
    "Buchberger_S_pair": 3,
    "commuting_five_dimensional_representation": 1,
    "representation_defining_relation": 1,
    "normal_form_vs_matrix": 81,
    "maximal_ideal_filtration": 1,
    "graded_dimensions": 1,
    "complete_initial_ideal_standard_basis": 144,
    "local_jet_dimension": 52,
    "origin_Jacobian": 4,
    "fiber_multiplication": 5,
    "conductor_complete_membership": 10935,
    "fiber_remainder_times_t": 10935,
    "conductor_generators_all_degrees": 150,
    "cusp_nilpotent_fiber": 1,
    "node_fiber_idempotents": 2,
    "conductor_tail_certificate": 47,
    "conductor_minimality_witness": 930,
    "semigroup_tail_membership": 7207,
    "conductor_A_generators": 7207,
    "homogeneous_differential_kernel_rank": 5154,
    "differential_relation_maps_zero": 1694,
    "differential_finite_tail_certificate": 764,
    "tested_two_generator_torsion_dimension": 47,
    "tau_annihilator_ideal": 24,
    "tau_spans_complete_kernel": 40,
    "assigned_torsion_length": 2,
    "assigned_differential_cokernel": 2,
    "assigned_annihilator_basis": 2,
    "positive_characteristic_torsion_changes": 2,
    "conductor_quotient_not_fiber": 1
  },
  "arithmetic": "exact integers/Fraction, plus explicitly named finite characteristics",
  "scope": {
    "quadratic_subring_polynomial_tests": 10935,
    "two_generator_semigroups": 47,
    "local_jet_orders": [
      0,
      1,
      2,
      3,
      4,
      5,
      6,
      7,
      8,
      9,
      10,
      11,
      12
    ]
  },
  "artinian_counterexample": {
    "basis": [
      "1",
      "x",
      "y",
      "y^2",
      "y^3"
    ],
    "ideal_power_dimensions": [
      5,
      4,
      2,
      1,
      0,
      0,
      0
    ],
    "associated_graded_relation": [
      "X^2",
      "XY",
      "Y^4"
    ]
  },
  "local_jet_lengths": {
    "parabola": [
      1,
      2,
      3,
      4,
      5,
      6,
      7,
      8,
      9,
      10,
      11,
      12,
      13
    ],
    "cusp": [
      1,
      3,
      5,
      7,
      9,
      11,
      13,
      15,
      17,
      19,
      21,
      23,
      25
    ],
    "node": [
      1,
      3,
      5,
      7,
      9,
      11,
      13,
      15,
      17,
      19,
      21,
      23,
      25
    ],
    "three_four": [
      1,
      3,
      6,
      9,
      12,
      15,
      18,
      21,
      24,
      27,
      30,
      33,
      36
    ]
  },
  "assigned_curves": [
    {
      "generators": [
        2,
        3
      ],
      "conductor": 2,
      "gaps": [
        1
      ],
      "torsion_weights": [
        5,
        7
      ],
      "annihilator_quotient_exponents": [
        0,
        2
      ],
      "cokernel_dt_exponents": [
        0
      ],
      "torsion_length_by_characteristic": {
        "2": 4,
        "3": 3,
        "5": 2,
        "7": 2
      }
    },
    {
      "generators": [
        3,
        4
      ],
      "conductor": 6,
      "gaps": [
        1,
        2,
        5
      ],
      "torsion_weights": [
        7,
        10,
        11,
        13,
        14,
        17
      ],
      "annihilator_quotient_exponents": [
        0,
        3,
        4,
        6,
        7,
        10
      ],
      "cokernel_dt_exponents": [
        0,
        1,
        4
      ],
      "torsion_length_by_characteristic": {
        "2": 8,
        "3": 9,
        "5": 6,
        "7": 6
      }
    }
  ],
  "tested_semigroups": [
    {
      "a": 2,
      "b": 3,
      "conductor": 2,
      "delta": 1,
      "torsion_dimension": 2
    },
    {
      "a": 2,
      "b": 5,
      "conductor": 4,
      "delta": 2,
      "torsion_dimension": 4
    },
    {
      "a": 2,
      "b": 7,
      "conductor": 6,
      "delta": 3,
      "torsion_dimension": 6
    },
    {
      "a": 2,
      "b": 9,
      "conductor": 8,
      "delta": 4,
      "torsion_dimension": 8
    },
    {
      "a": 2,
      "b": 11,
      "conductor": 10,
      "delta": 5,
      "torsion_dimension": 10
    },
    {
      "a": 2,
      "b": 13,
      "conductor": 12,
      "delta": 6,
      "torsion_dimension": 12
    },
    {
      "a": 2,
      "b": 15,
      "conductor": 14,
      "delta": 7,
      "torsion_dimension": 14
    },
    {
      "a": 3,
      "b": 4,
      "conductor": 6,
      "delta": 3,
      "torsion_dimension": 6
    },
    {
      "a": 3,
      "b": 5,
      "conductor": 8,
      "delta": 4,
      "torsion_dimension": 8
    },
    {
      "a": 3,
      "b": 7,
      "conductor": 12,
      "delta": 6,
      "torsion_dimension": 12
    },
    {
      "a": 3,
      "b": 8,
      "conductor": 14,
      "delta": 7,
      "torsion_dimension": 14
    },
    {
      "a": 3,
      "b": 10,
      "conductor": 18,
      "delta": 9,
      "torsion_dimension": 18
    },
    {
      "a": 3,
      "b": 11,
      "conductor": 20,
      "delta": 10,
      "torsion_dimension": 20
    },
    {
      "a": 3,
      "b": 13,
      "conductor": 24,
      "delta": 12,
      "torsion_dimension": 24
    },
    {
      "a": 3,
      "b": 14,
      "conductor": 26,
      "delta": 13,
      "torsion_dimension": 26
    },
    {
      "a": 4,
      "b": 5,
      "conductor": 12,
      "delta": 6,
      "torsion_dimension": 12
    },
    {
      "a": 4,
      "b": 7,
      "conductor": 18,
      "delta": 9,
      "torsion_dimension": 18
    },
    {
      "a": 4,
      "b": 9,
      "conductor": 24,
      "delta": 12,
      "torsion_dimension": 24
    },
    {
      "a": 4,
      "b": 11,
      "conductor": 30,
      "delta": 15,
      "torsion_dimension": 30
    },
    {
      "a": 4,
      "b": 13,
      "conductor": 36,
      "delta": 18,
      "torsion_dimension": 36
    },
    {
      "a": 4,
      "b": 15,
      "conductor": 42,
      "delta": 21,
      "torsion_dimension": 42
    },
    {
      "a": 5,
      "b": 6,
      "conductor": 20,
      "delta": 10,
      "torsion_dimension": 20
    },
    {
      "a": 5,
      "b": 7,
      "conductor": 24,
      "delta": 12,
      "torsion_dimension": 24
    },
    {
      "a": 5,
      "b": 8,
      "conductor": 28,
      "delta": 14,
      "torsion_dimension": 28
    },
    {
      "a": 5,
      "b": 9,
      "conductor": 32,
      "delta": 16,
      "torsion_dimension": 32
    },
    {
      "a": 5,
      "b": 11,
      "conductor": 40,
      "delta": 20,
      "torsion_dimension": 40
    },
    {
      "a": 5,
      "b": 12,
      "conductor": 44,
      "delta": 22,
      "torsion_dimension": 44
    },
    {
      "a": 5,
      "b": 13,
      "conductor": 48,
      "delta": 24,
      "torsion_dimension": 48
    },
    {
      "a": 5,
      "b": 14,
      "conductor": 52,
      "delta": 26,
      "torsion_dimension": 52
    },
    {
      "a": 6,
      "b": 7,
      "conductor": 30,
      "delta": 15,
      "torsion_dimension": 30
    },
    {
      "a": 6,
      "b": 11,
      "conductor": 50,
      "delta": 25,
      "torsion_dimension": 50
    },
    {
      "a": 6,
      "b": 13,
      "conductor": 60,
      "delta": 30,
      "torsion_dimension": 60
    },
    {
      "a": 7,
      "b": 8,
      "conductor": 42,
      "delta": 21,
      "torsion_dimension": 42
    },
    {
      "a": 7,
      "b": 9,
      "conductor": 48,
      "delta": 24,
      "torsion_dimension": 48
    },
    {
      "a": 7,
      "b": 10,
      "conductor": 54,
      "delta": 27,
      "torsion_dimension": 54
    },
    {
      "a": 7,
      "b": 11,
      "conductor": 60,
      "delta": 30,
      "torsion_dimension": 60
    },
    {
      "a": 7,
      "b": 12,
      "conductor": 66,
      "delta": 33,
      "torsion_dimension": 66
    },
    {
      "a": 7,
      "b": 13,
      "conductor": 72,
      "delta": 36,
      "torsion_dimension": 72
    },
    {
      "a": 7,
      "b": 15,
      "conductor": 84,
      "delta": 42,
      "torsion_dimension": 84
    },
    {
      "a": 8,
      "b": 9,
      "conductor": 56,
      "delta": 28,
      "torsion_dimension": 56
    },
    {
      "a": 8,
      "b": 11,
      "conductor": 70,
      "delta": 35,
      "torsion_dimension": 70
    },
    {
      "a": 8,
      "b": 13,
      "conductor": 84,
      "delta": 42,
      "torsion_dimension": 84
    },
    {
      "a": 8,
      "b": 15,
      "conductor": 98,
      "delta": 49,
      "torsion_dimension": 98
    },
    {
      "a": 9,
      "b": 10,
      "conductor": 72,
      "delta": 36,
      "torsion_dimension": 72
    },
    {
      "a": 9,
      "b": 11,
      "conductor": 80,
      "delta": 40,
      "torsion_dimension": 80
    },
    {
      "a": 9,
      "b": 13,
      "conductor": 96,
      "delta": 48,
      "torsion_dimension": 96
    },
    {
      "a": 9,
      "b": 14,
      "conductor": 104,
      "delta": 52,
      "torsion_dimension": 104
    }
  ],
  "limitations": [
    "Finite algebra certificates do not prove normalization of arbitrary input curves.",
    "General universal properties, support equivalence and localization are proved in prose.",
    "The two-generator torsion comparisons are finite tests; no identity for all curve singularities is inferred."
  ]
}