s1237 — the involution table, the charge conjugation, the real-form datum, the gauge orbit
receipts {'s1225': '3a34d719cd256201', 's787': '24034f3679056ba7', 's1221': '223df3ac5e9efa17', 's1220': '516a5537c347cd72', 's121a': 'af01f1b96491c5ac', 'substrate': '43341215b5224b20'}
  O   {'type': 'anti-symplectic', 'square': '+I', 'D56': '-D56', 'Z': '+Z', 'X': '+X'}
  T   {'type': 'symplectic', 'square': '-I', 'D56': '-D56', 'Z': '+Z', 'X': 'other'}
  W   {'type': 'anti-symplectic', 'square': '+I', 'D56': '+D56', 'Z': '+Z', 'X': 'other', 'signature_27': [12, 15]}
  EZ  {'type': 'symplectic', 'square': '+I', 'D56': '+D56', 'Z': '+Z', 'X': '+X', 'signature_27': [15, 12]}
  R   {'type': 'symplectic', 'square': '+I', 'D56': '+D56', 'Z': '-Z', 'X': '-X', 'signature_27': [15, 12]}
  C   {'type': 'symplectic', 'square': '+I', 'D56': '+D56', 'Z': '-Z', 'X': '+X', 'signature_27': [12, 15]}
  app_H_axes                 {'sigma_C': {'involution': True, 'form': 'isometry', 'signature_27': [11, 16]}, 'sigma_sig': {'involution': True, 'form': 'neither', 'signature_27': [18, 9]}, 'sigma_em_is_antisymplectic_involution': True}
  s787_trace_form_signature  [15, 12]
  EZ_commutant_grade0        {'dim': 39, 'compact': 16, 'noncompact': 23, 'grade0_dim': 79}
  gauge_orbit                {'dim': 12, 'trace_form_signature_of_the_gauge_algebra': [12, 16]}
  trace_form                 {'N_at_E': 6.0, 'signature': [15, 12], 'joint_signature_sign_tau_and_exp_pi_Z': {'-1,-1': 6, '-1,+1': 6, '+1,-1': 6, '+1,+1': 9}}
  receipt   PASS s1225_is_the_filed_evaluator_kernel_executed_head_only
  receipt   PASS s787_is_the_filed_App_H_kernel_whose_definitions_are_executed
  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 Z1_types_of_O_T_and_W
  computed  PASS Z2_types_of_the_charge_half_turn_and_of_the_end_reflection_R
  computed  PASS Z3_C_equals_minus_R_is_a_charge_conjugation_and_a_symmetry_of_the_gauging
  computed  PASS Z4_the_half_turn_of_the_charge_is_the_real_form_datum_and_the_embedding_image_is_its_graph
  computed  PASS Z5_App_H_throat_and_sheet_axes_are_not_conjugate_to_any_grade_preserving_element_of_the_table
  computed  PASS Z6_gauge_orbit_of_o_is_twelve_dimensional_with_complex_structure_ad_Z_reversed_by_C
  computed  PASS Z7_half_turn_of_the_charge_preserves_the_trace_form_at_the_neutral_unit_but_is_not_its_sign_operator
  argument  ARG  reading_the_charge_and_the_4_4_blocks
  argument  ARG  reading_two_bits_versus_App_H
  argument  ARG  reading_charge_conjugation
  argument  ARG  hat_tip_Wyler

VERDICT END flip = s787's σ_em axis (realised by O); PRESENTATION flip W has signature (12,15) on the 27 vs App H σ_C (11,16) and σ_sig (18,9): not conjugate — the two ℤ₂×ℤ₂ differ; exp(πZ) = diag(η_iη_j): the real-form datum is the half-turn of the charge and im Θ is its graph; C = −R: symplectic, compact, Z ↦ −Z, X ↦ +X — a charge conjugation symmetry; gauge orbit of o: dim 12, complex structure ad Z, reversed by C
RESULT_HASH e6dfc608554db38a
s1237: 11 computed, 7 receipt, 4 argument, 0 failed
