environment = {'python': '3.13.5', 'sympy': '1.14.0'}
data_basis = Positive root phi of t^2-t-1; declared H3(CD-split).
golden.polynomial_residual = 0
golden.reciprocal_square_sum = 3
golden.determinant = 1
golden.adjoint_diagonal = (-1/2 + sqrt(5)/2, 1, 1/2 + sqrt(5)/2)
golden.Gram = [[4, 3], [3, 4]]
golden.Gram_determinant = 7
golden.mismatch_cosine_squared = 9/16
golden.mismatch_sine_squared = 7/16
dimensions.octonion_Jordan_frame = (8, 27, 3)
dimensions.ratio = 8/3
normalization.off_diagonal_unit_trace_square = 2
normalization.chosen_three_copy_vector_square = 3
normalization.product = sqrt(6)/6
normalization.generations = The three-copy readout is stipulated, not derived here.
reciprocal_family.determinant = 1
reciprocal_family.Gram_determinant = (r - 1)**2*(r + 1)**2*(r**4 + 4*r**2 + 1)/r**4
negative_control.r3over2.Gram_determinant = 6025/1296
negative_control.r3over2.mismatch_sine_squared = 6025/17689
DET7_equal_norm_control.q_quadratic_residual = 0
DET7_equal_norm_control.actual_determinant_and_pairing = (1, 3)
DET7_equal_norm_control.positive_u_cubed = sqrt(105)/4 + 11/4
DET7_equal_norm_control.defining_polynomial = 2*u**6 - 11*u**3 + 2
DET7_equal_norm_control.Gram_product_mod_polynomial = 0
DET7_equal_norm_control.gcd_with_norm_equals4 = 1
DET7_equal_norm_control.conclusion = Unit determinant and Gram determinant 7 do not alone imply each squared norm is 4.
registered_C1_coefficient_proof = NOT VERIFIED: source formula only; A558 matrices absent.
registered_generator_uniqueness = NOT VERIFIED: A603/E110 construction absent.
finite_trace_Frobenius_proof = NOT TESTED by this script; see companion C08.2, not dim/rank arithmetic.
physical_attachment = NOT COMPUTED; no angle, mass or generation assignment inferred.