s1240 — the e7 bracket is a normed triality on the three real eights
receipts {'s1239': '5a5c62f3770072d8'}
  commutant    {'dim': 28, 'symmetric': 16, 'antisymmetric': 12, 'trace_form_signature': [16, 12], 'centre_dim': 0, 'intersection_with_gauge_algebra_dim': 4}
  eights       {'dims': [8, 8, 8], 'form_signatures': [[4, 4], [4, 4], [4, 4]], 'commutant_rank_on_each': [28, 28, 28]}
  composition  {'constant': [0.25, 0.25, 0.25], 'residual_below_1e-12': [True, True, True], 'adjoint_block_form_signature': [[4, 4], [4, 4], [4, 4]], 'control_other_weight_blocks_min_residual': 0.976, 'control_random_maps_residual': 0.991}
  algebra      {'norm_signature': [4, 4], 'unit_norm': 1.0, 'left_multiplication_rank_of_a_null_element': 4}
  derivations  {'dim': 14, 'killing_signature': [8, 6]}
  charges      {'pairing_of_each_eight': [[[0, 1], [2, 3]], [[0, 2], [1, 3]], [[0, 3], [1, 2]]], 'half_turn_eigenspace_signatures': [(2, 2)], 'T0_fixed_vectors_per_eight': [0, 0, 0]}
  receipt   PASS s1239_is_the_filed_kernel_whose_head_supplies_T0_and_the_three_planes
  receipt   PASS s1225_is_the_filed_evaluator_kernel_executed_head_only
  receipt   PASS s1235_is_the_filed_kernel_whose_charge_construction_is_copied
  receipt   PASS s1238_is_the_filed_house_check_of_the_lanes_point_c_c
  receipt   PASS the_filed_A1764_lane_report_is_the_source_of_B_c_and_of_the_lattice_weights_NOT_imported
  receipt   PASS s1220_is_the_filed_kernel_whose_construction_is_copied
  receipt   PASS s121a_is_the_file_whose_potential_is_copied
  computed  PASS the_two_generator_stacks_agree
  computed  PASS golden_vacuum_is_a_Minkowski_critical_point_as_s121a_says
  computed  PASS golden_vacuum_is_2lnphi_from_the_origin
  receipt   PASS s640_lib_is_the_S220_A_layer_executed_verbatim
  receipt   PASS s646_is_the_source_of_the_SV_vector_operator_executed_verbatim
  receipt   PASS s645c_results_hold_the_P6_gradient_reproduced_here
  computed  PASS the_S220_frame_is_this_kernels_frame
  computed  PASS Z0_the_torus_T0_its_fixed_directions_p0_and_three_commuting_sl2R_planes
  computed  PASS Z0_the_commutant_of_the_three_planes_is_so44_and_each_plane_carries_a_real_eight_with_an_invariant_44_form
  computed  PASS Z1_the_e7_action_between_the_eights_obeys_the_composition_law_for_the_three_44_forms
  computed  PASS Z2_a_unital_alternative_nonassociative_composition_algebra_of_dimension_eight_with_isotropic_norm
  computed  PASS Z3_the_derivation_algebra_has_dimension_14_and_killing_signature_8_6_the_split_form_of_g2
  computed  PASS Z4_each_eight_carries_one_pairing_of_the_four_weights_the_half_turn_splits_44_into_22_plus_22_and_no_vector_is_fixed_by_the_torus
  argument  ARG  classification
  argument  ARG  reading

VERDICT commutant of the three planes = so(4,4) (28; trace form (16,12)); three real eights with invariant (4,4) forms; the e7 action A_(i→j) × U_i → U_j obeys the composition law (c = 1/4, three cyclic maps); with units: a unital alternative non-associative composition algebra, N of signature (4,4), Der of dimension 14 with Killing signature (8, 6) — the split octonions by classification; T0 fixes no vector of any eight
RESULT_HASH d4780902674500e8
s1240: 10 computed, 10 receipt, 2 argument, 0 failed
