{
  "status": "PASS",
  "checks": 7523,
  "groups": {
    "universal_Pascal_dot_polynomial": 3,
    "universal_Pascal_converse_determinant_polynomial": 1,
    "symmetric_square_determinant_polynomial": 1,
    "nonorthogonal_model_matrix_determinant": 48,
    "complete_parameter_points_distinct": 48,
    "constructed_congruence_coefficient_identity": 48,
    "constructed_basis_invertible": 48,
    "transformed_parameter_on_conic": 424,
    "original_parameter_inverse": 424,
    "constructed_parameter_inverse_cover": 424,
    "tangent_dual_quadric_and_contact": 424,
    "pole_polar_inverse": 424,
    "distinct_chord_nonzero": 376,
    "secant_harmonic_polar_incidence": 376,
    "harmonic_crossratio_minus_one": 376,
    "five_points_recover_original_conic": 80,
    "five_point_constraint_rank": 80,
    "Pascal_all_three_incidences": 761,
    "Pascal_three_distinct_meets": 761,
    "Brianchon_all_three_incidences": 761,
    "Brianchon_three_distinct_diagonals": 761,
    "Brianchon_point_is_Pascal_pole": 40,
    "four_point_crossratio_invariant": 48,
    "finite_field_entire_plane_zero_locus_equals_parameters": 40,
    "all_720_orders_polar_duality_over_F5": 720,
    "capstone_recovered_H": 1,
    "capstone_rank_five_minor": 1,
    "capstone_ten_noncollinearity_determinants": 1,
    "capstone_Pascal_line_Brianchon_point": 1,
    "capstone_three_polar_lines": 1,
    "quadratic_field_tangent_coefficients": 6,
    "quadratic_field_contact_on_conic": 2,
    "quadratic_field_tangent_through_rational_point": 2,
    "projective_infinity_migration": 1,
    "four_point_compatible_target": 1,
    "four_point_incompatible_target": 1,
    "mod_three_obstruction_first_stage": 1,
    "invalid_input_rejected": 7
  },
  "field_models": {
    "Q": 8,
    "3": 8,
    "5": 8,
    "7": 8,
    "11": 8,
    "13": 8
  },
  "ordered_hexagons_F5": 720,
  "scope": "Exact field operations; coefficientwise polynomial identities and finite model tests. General proofs and the rational nonexistence descent are in the prose. Arithmetic-operation counts are not bit-cost bounds.",
  "capstone": {
    "points": [
      [
        0,
        1,
        1
      ],
      [
        1,
        0,
        1
      ],
      [
        1,
        1,
        1
      ],
      [
        3,
        6,
        5
      ],
      [
        2,
        6,
        5
      ],
      [
        0,
        0,
        1
      ]
    ],
    "five_point_rows": [
      [
        "0",
        "1",
        "1",
        "0",
        "0",
        "1"
      ],
      [
        "1",
        "0",
        "1",
        "0",
        "1",
        "0"
      ],
      [
        "1",
        "1",
        "1",
        "1",
        "1",
        "1"
      ],
      [
        "9",
        "36",
        "25",
        "18",
        "15",
        "30"
      ],
      [
        "4",
        "36",
        "25",
        "12",
        "10",
        "30"
      ]
    ],
    "kernel": [
      1,
      1,
      0,
      0,
      -1,
      -1
    ],
    "triple_determinants": [
      "1",
      "4",
      "3",
      "1",
      "1",
      "1",
      "2",
      "3",
      "6",
      "1"
    ],
    "H": [
      [
        -2,
        0,
        1
      ],
      [
        0,
        -2,
        1
      ],
      [
        1,
        1,
        0
      ]
    ],
    "H_inverse": [
      [
        "-1/4",
        "1/4",
        "1/2"
      ],
      [
        "1/4",
        "-1/4",
        "1/2"
      ],
      [
        "1/2",
        "1/2",
        "1"
      ]
    ],
    "edges": [
      [
        1,
        1,
        -1
      ],
      [
        1,
        0,
        -1
      ],
      [
        1,
        2,
        -3
      ],
      [
        0,
        5,
        -6
      ],
      [
        3,
        -1,
        0
      ],
      [
        1,
        0,
        0
      ]
    ],
    "Pascal_points": [
      [
        1,
        -6,
        -5
      ],
      [
        1,
        3,
        1
      ],
      [
        0,
        3,
        2
      ]
    ],
    "Pascal_line": [
      3,
      -2,
      3
    ],
    "tangents": [
      [
        1,
        -1,
        1
      ],
      [
        1,
        -1,
        -1
      ],
      [
        1,
        1,
        -2
      ],
      [
        1,
        7,
        -9
      ],
      [
        1,
        -7,
        8
      ],
      [
        1,
        1,
        0
      ]
    ],
    "vertices": [
      [
        1,
        1,
        0
      ],
      [
        3,
        1,
        2
      ],
      [
        5,
        7,
        6
      ],
      [
        7,
        17,
        14
      ],
      [
        1,
        -1,
        -1
      ],
      [
        1,
        -1,
        -2
      ]
    ],
    "diagonals": [
      [
        7,
        -7,
        5
      ],
      [
        1,
        5,
        -4
      ],
      [
        2,
        -4,
        3
      ]
    ],
    "Brianchon_point": [
      1,
      11,
      14
    ],
    "polars": [
      [
        1,
        -1,
        0
      ],
      [
        3,
        -3,
        -1
      ],
      [
        0,
        0,
        1
      ]
    ],
    "infinite_intersection": [
      1,
      -6,
      0
    ],
    "crossratios": {
      "source": "1/2",
      "bad_target": "2/3"
    }
  }
}