{
  "status": "PASS",
  "assertions": 287679,
  "categories": {
    "E1_complete_height_two_box": 1,
    "E1_first_squareclasses": 1,
    "E1_larger_box_regression_only": 1,
    "E1_second_layer_non_double": 2,
    "E1_torsion_translation_height": 17673,
    "E3_local_quartic_obstruction": 792,
    "E5_first_double": 1,
    "E5_non_torsion_threshold": 1,
    "E5_repeated_height_growth": 5,
    "E5_two_preimages": 2,
    "finite_field_correction_square_test": 300,
    "finite_field_dual_kernel": 300,
    "finite_field_exact_index_formula": 300,
    "finite_field_first_composite": 3616,
    "finite_field_first_homomorphism": 48816,
    "finite_field_first_kernel": 300,
    "finite_field_first_squareclass_kernel": 3616,
    "finite_field_image_equations": 300,
    "finite_field_second_composite": 3616,
    "finite_field_second_squareclass_kernel": 3616,
    "finite_field_squareclass_homomorphism": 48816,
    "height_doubling_bounds": 61675,
    "height_gcd_divisibility": 61675,
    "height_paired_addition_bound": 396,
    "height_symmetric_pair_lemma": 30976,
    "quartic_zero_denominator": 16,
    "quartic_zero_numerator": 8,
    "rational_composite": 40,
    "rational_dual_preimage": 6,
    "rational_first_image": 40,
    "rational_homomorphism": 248,
    "rational_quartic_forward": 24,
    "rational_quartic_reverse": 38,
    "rational_squareclass_homomorphism": 248,
    "rational_squarefree_support": 40,
    "reject_missing_dual_scaling": 1,
    "reject_missing_kernel_correction": 167,
    "reject_one_sided_y_sign": 1,
    "symbolic_doubling_y": 1,
    "symbolic_dual_composite_y": 1,
    "symbolic_paired_addition_product": 1,
    "symbolic_paired_addition_sum": 1,
    "symbolic_target_equation": 1
  },
  "details": {
    "models": 300,
    "kernel_correction_model_counts": {
      "1": 133,
      "2": 167
    },
    "rational_models": 8,
    "rational_points_in_height_36_boxes": 40,
    "primitive_height_inputs": 61675,
    "E1_rational_points_proved_in_text": [
      "O",
      [
        0,
        0
      ],
      [
        1,
        0
      ],
      [
        -1,
        0
      ]
    ],
    "E5_first_five_doubling_heights": [
      "25",
      "1681",
      "11183412793921",
      "62425319345774489875576913540908007654663493663770881",
      "15186149480603561077873486951173749559525479302211996827405127217678870732032108537181044477898873408310514497391618637431614257333642103164013127658012672837118280294149649202051220990692972277960589780132766721"
    ],
    "finite_search_scope": "Only bounded-height boxes are enumerated; completeness uses the text descent proof."
  }
}