environment = Python 3.13.5; SymPy 1.14.0
arithmetic = exact rationals / symbolic polynomials / algebraic radicals
universal_square_root_residual = 0
universal_inverse_residual = 0
model_U = [[1, 1], [0, 1]]
model_V = [[1, 0], [-1, 1]]
model_hyperbolic_word = [[2, 1], [1, 1]]
model_word_characteristic = lambda**2 - 3*lambda + 1
model_braid_residual_zero = True
model_central_cube = Matrix([[-1, 0], [0, -1]])
model_square_root = [[3*sqrt(5)/5, sqrt(5)/5], [sqrt(5)/5, 2*sqrt(5)/5]]
model_root_trace_and_determinant = (sqrt(5), 1)
model_Clifford_squares = ['I', 'I', '-I']
symbolic_model_Gram_residual_zero = True
nonorthogonal_Clifford_control_Gram = [[1/24, 0], [0, 1/96]]
Clifford_relations_alone_force_Frobenius_isotropy = False
conditional_model_active_inactive_dimensions = (24, 32)
conditional_model_central_eigenvalue_multiplicities = {-1: 24, 1: 32}
conditional_model_global_projectivization_to_PSL2Z = False
unit_column_Gram_coefficients = {1: 1/24, 10: 5/12}
Z4_arithmetic_mirror_checks = 16
Z4_checks_are_registered_generator_census = False
registered_frame_tick_cylinder_winding_scale = NOT VERIFIED: frozen matrices / cochain complex absent
result = PASS: universal polynomial implications and explicitly marked standard models