s1260 — the D_KK grading and the two ladder twists
  level0            {"spec D_KK": [[-6.0, 1], [-2.0, 27], [2.0, 27], [6.0, 1]], "D_KK symmetric": "<1e-12", "[B1, D_KK] / ‖D_KK‖": "<1e-12", "[B2, D_KK] / ‖D_KK‖": "<1e-12", "[W_h, D_KK] / ‖D_KK‖": "<1e-12", "grades of B1 − I": {"0": 1.0}, "grades of W_h − I": {"0": 1.0}}
  discrete_on_D_KK  {"O": {"+": "7.071e-01", "−": "<1e-12"}, "C56": {"+": "2.711e-01", "−": "4.360e-01"}, "CP": {"+": "4.360e-01", "−": "2.711e-01"}}
  ladder_parity     {"G² − B1B2⁻¹": "<1e-12", "Gⁿ on D_KK": {"1": "reverses", "2": "preserves", "3": "reverses", "4": "preserves"}}
  odd_rung_trace    {"M_G (homology factor of G)": [[1.0, 1.0], [1.0, 0.0]], "tensor rank-1": "<1e-09", "per n": {"1": {"tr M_Gⁿ": 1.0, "γ_n": 1.0, "equal": true, "tr(Gⁿ|act)": 0.0}, "2": {"tr M_Gⁿ": 3.0, "γ_n": 2.236067977, "equal": false, "tr(Gⁿ|act)": 36.0}, "3": {"tr M_Gⁿ": 4.0, "γ_n": 4.0, "equal": true, "tr(Gⁿ|act)": 0.0}, "4": {"tr M_Gⁿ": 7.0, "γ_n": 6.708203932, "equal": false, "tr(Gⁿ|act)": 84.0}, "5": {"tr M_Gⁿ": 11.0, "γ_n": 11.0, "equal": true, "tr(Gⁿ|act)": 0.0}, "6": {"tr M_Gⁿ": 18.0, "γ_n": 17.88854382, "equal": false, "tr(Gⁿ|act)": 216.0}}}
  two_gradings      {"D56 − R·D_KK·Rᵀ": "<1e-12", "R orthogonal": "<1e-12", "R symplectic": "<1e-12", "[D56, D_KK]": "<1e-12", "[golden generator, D_KK] / ‖D_KK‖": "3.121e-02", "[golden generator, D56] / ‖D56‖": "<1e-12", "[golden boost, D56] / ‖D56‖": "<1e-12", "[B1, D56] / ‖D56‖": "2.357e-01", "[G², D56] / ‖D56‖": "2.357e-01", "O D56 O⁻¹ + D56": "<1e-12", "[C56, D56]": "<1e-12", "grades (D_KK) of the golden generator": {"-4": 0.033715, "0": 0.932569, "4": 0.033715}}
  fermion8          {"O8·Ō8 + I": "<1e-12", "CP8·C̄P8 − I": "<1e-12", "C8² − I": "<1e-12", "real fixed dim of ψ ↦ O8ψ̄": 0, "real fixed dim of ψ ↦ CP8ψ̄": 8, "C8 eigenvalues": [[-1.0, 4], [1.0, 4]]}
  vocabulary        {"forbidden-token hits in this file": 0, "control (each token once)": 5}
  receipt   PASS filed_s1026_LANE_D1192_LENS_ARTIFACTS_npz
  receipt   PASS filed_d1410_solder_npz
  receipt   PASS filed_d1409_generators_npz
  receipt   PASS filed_d1412_house_frames_npz
  receipt   PASS filed_chatgpt_d1411_maps_npz
  receipt   PASS s1257_results_hold_the_rung_couplings
  computed  PASS K1_the_registered_braid_representation_lies_in_the_level_zero_Levi_of_D_KK
  computed  PASS K2_O_reverses_D_KK_and_C56_CP_map_it_to_neither_sign
  computed  PASS K3_odd_powers_of_G_reverse_D_KK_even_powers_preserve_it
  computed  PASS K4_gamma_n_is_the_trace_of_the_n_th_power_of_Gs_homology_factor_on_odd_rungs_only_and_the_full_odd_trace_vanishes
  computed  PASS K5_the_shell_golden_boost_is_level_zero_for_D56_not_for_D_KK_and_the_braid_is_level_zero_for_D_KK_not_for_D56
  computed  PASS K5b_O_reverses_D56_too_and_C56_preserves_D56
  computed  PASS K6_the_end_flip_has_no_fixed_fermion_CP_gives_a_real_form_C56_a_linear_4_4_split
  computed  PASS V1_no_momentum_vocabulary_for_D_KK_in_this_file
  argument  ARG  the_two_ladders_in_the_grading
  argument  ARG  odd_rungs_and_orbifold
  argument  ARG  scope
VERDICT the registered braid representation is level 0 for D_KK; O and G = B₁·O reverse D_KK, so odd rungs are grading reflections and even rungs (figure-8 words) level-0; γ_n = tr M_Gⁿ on odd rungs only; the shell golden boost is level 0 for the commuting grading D56 = R·D_KK·Rᵀ, not for D_KK — two twists, two gradings; the end flip fixes no fermion of the 8.
RESULT_HASH 74b6d9a445964602
s1260: 8 computed, 6 receipt, 3 argument, 0 failed
