{
  "status": "PASS",
  "checks": 2284,
  "categories": {
    "index1_initial_constraint": 5,
    "index1_initial_derivative": 5,
    "index1_branch_discriminant": 100,
    "index1_backward_euler_differential": 100,
    "index1_backward_euler_constraints": 100,
    "index1_branch_order": 100,
    "index1_newton_determinant": 100,
    "terminal_initial_derivative": 1,
    "terminal_coupled_step": 1,
    "terminal_step_determinant": 1,
    "terminal_exact_quadratic_product": 1,
    "terminal_exact_quadratic_sum": 1,
    "terminal_exact_quadratic_step": 1,
    "nilpotent_derivative_array_minimality": 20,
    "regular_supplied_left_right": 17,
    "regular_invertible_factors": 17,
    "regular_polynomial_trajectory_identity": 63,
    "fitting_free_dimension": 17,
    "fitting_invertibility": 17,
    "fitting_algebraic_identity": 165,
    "fitting_nilpotent_exact_index": 15,
    "regular_pencil_determinants": 51,
    "fitting_differential_identity": 30,
    "fitting_cross_blocks": 90,
    "terminal_mixed_certificate": 1,
    "terminal_initial_vector": 1,
    "terminal_mixed_trajectory": 132,
    "high_frequency_consistent_initial_shift": 7,
    "high_frequency_small_data_large_state": 7,
    "high_frequency_original_equations": 336,
    "backward_euler_finite_inverse": 20,
    "backward_euler_impulse_exact_residual": 60,
    "backward_euler_impulse_finite_death": 20,
    "backward_euler_residual_to_error": 20,
    "backward_euler_chain_residual_gain": 20,
    "multiple_constraints_gram_positive": 9,
    "multiple_constraints_dynamic_row": 27,
    "multiple_constraints_feedback_row": 27,
    "terminal_ellipse_multiplier": 2,
    "terminal_ellipse_feedback": 2,
    "ellipse_physical_euler_drift": 6,
    "terminal_exp_lower_certificate": 1,
    "terminal_tolerance_rational_certificate": 1,
    "critical_forcing_convolution_identity": 45,
    "critical_forcing_differential_identity": 45,
    "critical_forcing_uniform_bound": 45,
    "constant_defect_exact_equation": 13,
    "constant_defect_initial_state": 1,
    "critical_jordan_nilpotency": 3,
    "critical_euler_jordan_power": 378,
    "critical_euler_zero_eigenvalue": 3,
    "critical_euler_boundary_growth": 33,
    "terminal_boundary_fourth_step": 1
  },
  "precision_digits": 80,
  "regular_pencil_models": 17,
  "multiple_constraint_cases": 27,
  "terminal": {
    "backward_euler": {
      "X": "2.56433348938823046532798534692665443477476897",
      "Z1": "2.69300046816469139598395604077996330432430692",
      "Z2": "0.371333021223539069344029306146691130450462056"
    },
    "feedback_exact_e_at_2": "0.00381727835206619197148955784345766855291997856",
    "feedback_defect_bound_at_2": "0.00382710483941382532639994468173751138616757311",
    "rational_bound": "154393/40000000",
    "tolerance": "1/250"
  },
  "scope": "Exact finite certificates and 80-digit diagnostics; continuous existence, index minimality and infinite-time stability rely on the written proofs."
}