python = 3.13.5 ; sympy = 1.14.0
negative_control_input_sha256 = cfdb7171c14cb9b7701f44095ddfcb8c8107d85845e74f52525d4637ff4453a3
basis_dimension = 8 ; quaternion_half_dimension = 4 ; quaternion_pair_dimension = 8 ; compact_octonion_pair_dimension = 16
basis_order = 1,e1,e2,e3,f1,f2,f3,l
| x*y | 1 | e1 | e2 | e3 | f1 | f2 | f3 | l |
|---|---|---|---|---|---|---|---|---|
| 1 | 1 | e1 | e2 | e3 | f1 | f2 | f3 | l |
| e1 | e1 | -1 | e3 | -e2 | l | -f3 | f2 | -f1 |
| e2 | e2 | -e3 | -1 | e1 | f3 | l | -f1 | -f2 |
| e3 | e3 | e2 | -e1 | -1 | -f2 | f1 | l | -f3 |
| f1 | f1 | -l | -f3 | f2 | 1 | e3 | -e2 | -e1 |
| f2 | f2 | f3 | -l | -f1 | -e3 | 1 | e1 | -e2 |
| f3 | f3 | -f2 | f1 | -l | e2 | -e1 | 1 | -e3 |
| l | l | f1 | f2 | f3 | e1 | e2 | e3 | 1 |
zorn_cd_signed_unit_checks = 64 ; negative_products = 24
two_sided_unit_basis_checks = 8
unordered_imaginary_anticommutation_checks = 21
basis_left_right_alternative_checks = 128
polarized_alternative_vector_checks = 1024
polarized_alternative_scalar_coefficients = 8192
symbolic_zorn_cd_coordinate_residuals = [0, 0, 0, 0, 0, 0, 0, 0]
symbolic_norm_composition_residual = 0
symbolic_norm_and_conjugation_residuals = [0, 0, 0, 0, 0, 0, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0] [0, 0, 0, 0, 0, 0, 0, 0]
norm_polynomial = E1**2 + E2**2 + E3**2 - F1**2 - F2**2 - F3**2 + s**2 - t**2
norm_matrix_diagonal = [1, 1, 1, 1, -1, -1, -1, -1] ; inertia(+,-,0) = [4, 4, 0]
basis_norms = [1, 1, 1, 1, -1, -1, -1, -1]
null_controls = {'N(1+l)': 0, 'N(1-l)': 0, '(1+l)(1-l)': '0', 'N((1+l)+(1-l))': 4, 'N(e1+f1)': 0, '(e1+f1)^2': '0'}
totally_null_plane b=v=0: free_coordinates = 4 ; norm = 0
nonassociative_witness [e1,e2,f1] = -2f2
sample_integer_pairs = 64 ; seed = 1256 ; coefficient_range = [-2, 2] ; all_assertions_passed = True
legacy_left_alternative_failures = 30 of 64
legacy_right_alternative_failures = 30 of 64
legacy_witness [e1,e1,e2] = -2e2
legacy_conjugation_candidate_diagonal = [1, 1, 1, 1, -1, -1, -1, 1] ; inertia(+,-,0) = [5, 3, 0]
legacy_N(e1*e2), N(e1)*N(e2) = -1 1
legacy_conjugation_candidate_residual = [0, 0, 0, 0, 0, 0, 0, 0]
SUITE_BANKED_ARRAY_ALIGNMENT = NOT VERIFIED