s1250 — the circle generators in the frozen 56 frame: clock, twist, KK singlets, periods and fermion lifts, the three SL(2) types
receipts {'s1239': '5a5c62f3770072d8'}
  carrier             {'compact_dim': 63, 'e7_dim': 133, 'grading_dims': [27, 79, 27], 'D56_levels': [(-6.0, 1), (-2.0, 27), (2.0, 27), (6.0, 1)]}
  clock_K             {'charges_56': [(-3.0, 1), (-1.0, 27), (1.0, 27), (3.0, 1)], 'charges_8': [(-0.5, 6), (1.5, 2)], 'exp_pi_K_is_minus_I56': True, 'exp_2pi_K8_is_minus_I8': True, 'appH_recipe_same_spectrum': [True, True, True]}
  twist_Z             {'centre_dim': 1, 'cos_to_centre': 1.0, 'charges_56': [(-1.0, 12), (0.0, 32), (1.0, 12)], 'charges_8': [(-0.5, 4), (0.5, 4)], 'goldstones': 12, 'hessian_spectrum': [(0.0, 48), (2.0, 20), (8.0, 2)], 'lambda_house_to_appG': 48.0, 'Z2_equals_q0_times_Z': True}
  kk_singlets         {'gauge_generator_is_pure_level0_and_parallel_to_Z': True, 'X_of_v_equals_c_times_Z': {'-6': -0.707106781, '6': -0.707106781}, 'preimage_support_is_the_two_singlets': True, 'electric_magnetic_split': {'-6': [0.5, 0.5], '6': [0.5, 0.5]}}
  gauge_algebra_at_o  {'dim': 28, 'levi_compact': 16, 'levi_span_is_stab_o': True, 'noncompact_mixed': 12, 'plus4_halves_rank': 12}
  periods             {'Z': {'charges_56': [(-1.0, 12), (0.0, 32), (1.0, 12)], 'charges_8': [(-0.5, 4), (0.5, 4)], 'eps': -1, 'lattice_k_over_48': [12, 24, 36, 48]}, 'K': {'charges_56': [(-3.0, 1), (-1.0, 27), (1.0, 27), (3.0, 1)], 'charges_8': [(-0.5, 6), (1.5, 2)], 'eps': -1, 'lattice_k_over_48': [24, 48]}, 'T1': {'charges_56': [(-1.0, 12), (0.0, 32), (1.0, 12)], 'charges_8': [(-1.0, 1), (0.0, 6), (1.0, 1)], 'eps': 1, 'lattice_k_over_48': [48]}, 'T2': {'charges_56': [(-1.0, 12), (0.0, 32), (1.0, 12)], 'charges_8': [(-1.0, 1), (0.0, 6), (1.0, 1)], 'eps': 1, 'lattice_k_over_48': [48]}, 'T3': {'charges_56': [(-1.0, 12), (0.0, 32), (1.0, 12)], 'charges_8': [(-1.0, 1), (0.0, 6), (1.0, 1)], 'eps': 1, 'lattice_k_over_48': [48]}, 'T4': {'charges_56': [(-1.0, 12), (0.0, 32), (1.0, 12)], 'charges_8': [(-1.0, 1), (0.0, 6), (1.0, 1)], 'eps': 1, 'lattice_k_over_48': [48]}}
  non_conjugacy       {'zeros_56': {'Z': 32, 'K': 0}, 'Z_vs_T_same_56': True, 'same_pairwise_sums_of_the_8': True, 'different_8': True, 'charges_70': {'Z': [(-2.0, 1), (-1.0, 16), (0.0, 36), (1.0, 16), (2.0, 1)], 'T1': [(-1.0, 20), (0.0, 30), (1.0, 20)], 'T2': [(-1.0, 20), (0.0, 30), (1.0, 20)], 'T3': [(-1.0, 20), (0.0, 30), (1.0, 20)], 'T4': [(-1.0, 20), (0.0, 30), (1.0, 20)]}}
  D56                 {'real_spectrum': True, 'leak_out_of_the_holomorphic_28': 1.0, 'unit_test_hits': {'phi': [], '1+sqrt2': [], '2+sqrt3': [], '2': [], '3': []}}
  receipt   PASS s1239_is_the_filed_kernel_whose_head_supplies_the_frozen_56_frame
  receipt   PASS s1249_is_the_filed_kernel_whose_lattice_frame_and_end_twist_are_continued
  receipt   PASS appendix_G_as_printed_holds_thm_kkform_q0_and_the_plus_minus_half_line
  receipt   PASS appendix_H_as_printed_holds_the_clock_K_spectrum
  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 C0_the_compact_algebra_is_63_dimensional_e7_is_133_and_ad_D56_grades_it_27_79_27
  computed  PASS C1_the_clock_K_is_a_spinor_circle_through_the_centre_of_E7_and_App_Hs_recipe_gives_the_same_class
  computed  PASS C2_Z_is_the_centre_of_stab_o_and_App_Gs_Z2_with_Z2_equal_q0KK_times_Z_and_its_fermion_charges_are_plus_minus_half
  computed  PASS C3_the_two_D56_singlet_vectors_gauge_exactly_the_twist_and_are_the_only_vectors_that_do
  computed  PASS C4_the_gauge_algebra_at_o_is_16_compact_Levi_plus_12_symmetric_generators_whose_level_plus_4_halves_are_commuting_nilpotents
  computed  PASS C5_periods_fermion_lifts_spinor_signs_and_the_lattice_subgroup_for_Z_K_and_the_four_torus_generators
  computed  PASS C6_Z_is_not_conjugate_to_K_and_Z_and_each_torus_generator_share_the_56_spectrum_but_differ_on_the_fermion_8_and_on_the_70
  computed  PASS C7_the_three_SL2_types_are_all_present_D56_has_no_fermion_lift_and_exp_tD56_is_not_integral_in_the_A1768_frame_for_the_tested_units
  argument  ARG  what_the_double_duty_question_now_rests_on
  argument  ARG  two_fourfold_objects_not_to_conflate
  argument  ARG  the_selfridge_straus_pair
  argument  ARG  scope

VERDICT K (App H's clock, Cartan-compatible) is a spinor circle through the centre of E7 (exp(πK) = −I₅₆; fermion weights −½ ×6, +3/2 ×2; exp(2πK₈) = −I₈); Z = ½ΣT is the centre of stab(o) and is App G's Z₂ = q₀^KK·Z (thm:kkform reproduced: H = −(q₀ ad Z)² on the Goldstone complement), fermion charges ±½; the two D56 = ±6 singlets gauge exactly Z and are the only vectors that do, each half electric / half magnetic; the gauge algebra at o is 16 compact Levi + 12 noncompact x₊ + x₊ᵀ with commuting nilpotent halves; Z and each T_a share the 56-spectrum (a Selfridge–Straus pair) and differ on the 8 and the 70, so Z is not conjugate to any T_a, nor to K; all three SL(2) types occur; D56 has no fermion lift and no tested unit makes exp(tD56) integral in the A1768 frame
RESULT_HASH 778a4d2c4bb50fe7
s1250: 13 computed, 13 receipt, 4 argument, 0 failed
