{
  "schema": "exact-course-calculation/v1",
  "lesson": "CG-S6-01",
  "passed": 45,
  "checks": [
    "case_1:exact_order",
    "case_1:fixed_columns",
    "case_1:fixed_dimension",
    "case_1:invariant_covector",
    "case_1:all_image_columns",
    "case_1:oriented_index_determinant",
    "case_1:inverse_lattice_coordinates",
    "case_1:period_covariance",
    "case_1:fixed_period",
    "case_1:delta_period",
    "case_1:moving_periods",
    "case_1:linear_cover_determinant",
    "case_1:kernel_lift",
    "case_1:kernel_exact_first_coordinate_order",
    "case_1:kernel_moving_coordinate_period",
    "case_1:rotation_lattice_matrix",
    "case_1:intertwining_linear",
    "case_1:intertwining_translation",
    "case_1:kernel_rotation_period",
    "case_1:only_identity_has_period_translation",
    "case_1:normal_character_exponent",
    "case_1:one_form_eigenvalues",
    "case_2:exact_order",
    "case_2:fixed_columns",
    "case_2:fixed_dimension",
    "case_2:invariant_covector",
    "case_2:all_image_columns",
    "case_2:oriented_index_determinant",
    "case_2:inverse_lattice_coordinates",
    "case_2:period_covariance",
    "case_2:fixed_period",
    "case_2:delta_period",
    "case_2:moving_periods",
    "case_2:linear_cover_determinant",
    "case_2:kernel_lift",
    "case_2:kernel_exact_first_coordinate_order",
    "case_2:kernel_moving_coordinate_period",
    "case_2:rotation_lattice_matrix",
    "case_2:intertwining_linear",
    "case_2:intertwining_translation",
    "case_2:kernel_rotation_period",
    "case_2:only_identity_has_period_translation",
    "case_2:normal_character_exponent",
    "case_2:one_form_eigenvalues",
    "full_real_period_determinant"
  ],
  "cases": [
    {
      "case": 1,
      "cover_degree": 3,
      "affine_order": 3,
      "composite_degree": 9,
      "determinant": -3
    },
    {
      "case": 2,
      "cover_degree": 2,
      "affine_order": 4,
      "composite_degree": 8,
      "determinant": -2
    }
  ],
  "source_sha256": "70dbb98c32f71b4c8e5cf664b365d63b6c10c7157d984de2d1b5b25316d5cd09",
  "method": "Exact SymPy expressions; no floating point tests.",
  "scope": "Displayed matrix, period, lattice, affine and character identities. Complete geometric proofs are in the lesson; no independent review or global sphere recognition is certified by this script."
}