s1264 — the bosonic hexagram frame on the registered arrays
  lines           {"Q_t^H T_a Q_t − Λ²(T8_a) (max)": "<1e-12", "Q_t^H K Q_t − Λ²(K8)": "<1e-12", "Z − ½ΣT": "<1e-12", "T8_a spectra": [[-1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0], [-1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0], [-1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0], [-1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]], "plane fixed by A13 and the cycle": [1], "labels {plane: bits}": {"1": [0, 0], "0": [0, 1], "2": [1, 0], "3": [1, 1]}, "Bm unitary": "<1e-12", "Z1 − exp(π Σ_{bit1} T8)": "<1e-12", "Z2 − exp(π Σ_{bit2} T8)": "<1e-12", "i·Z3 − exp(π Z8)": "<1e-12", "X3 − C8": "<1e-12"}
  weyl_roots      {"compact gauge dim": 16, "lift residual": "<1e-12", "roots": {"12": {"root-space dim": 2, "|Y₊ − Y₋|": "<1e-09", "[Y, X3] (basis)": "<1e-09"}, "03": {"root-space dim": 2, "|Y₊ − Y₋|": "<1e-09", "[Y, X3] (basis)": "<1e-09"}, "10": {"root-space dim": 2, "|Y₊ − Y₋|": "<1e-09", "[Y, X3] (basis)": "<1e-09"}, "23": {"root-space dim": 2, "|Y₊ − Y₋|": "<1e-09", "[Y, X3] (basis)": "<1e-09"}}}
  hexagram_group  {"charge line on the 56: Λ²(Z3) + exp(πZ) (E7 centre)": "<1e-12", "X3 line on the 56 − C56": "<1e-12", "involutions (max)": "<1e-12", "commutators (max)": "<1e-12", "distinct products": 64, "X-preservation (max relative)": "<1e-12", "[g, O] (max)": "<1e-12"}
  census          {"compact 63": {"distinct": 63, "profile {mult: count}": {"1": 63}, "trivial multiplicity": 0, "total": 63}, "noncompact 70": {"distinct": 64, "profile {mult: count}": {"1": 63, "7": 1}, "trivial multiplicity": 7, "total": 70}, "56": {"distinct": 28, "profile {mult: count}": {"2": 28}, "trivial multiplicity": 0, "total": 56}}
  pauli_pattern   {"anticommuting pairs (Z first)": ["Z1X1", "Z2X2", "Z3X3"], "neither": []}
  S3_action       {"A13": {"Z1": "Z1Z2", "Z2": "Z2", "zeta": "zeta", "C56": null}, "cycle": {"Z1": "Z2", "Z2": "Z1Z2", "zeta": "zeta", "C56": "C56"}}
  receipt   PASS filed_d1414_house_frames_npz
  receipt   PASS filed_d1409_generators_npz
  receipt   PASS filed_d1412_house_frames_npz
  receipt   PASS filed_d1410_solder_npz
  receipt   PASS s1263_is_the_filed_fermion_side_check
  computed  PASS H1_the_Z_lines_are_gauge_torus_elements_the_charge_line_is_the_centre_half_turn_and_X3_is_C8
  computed  PASS H2_six_registered_symmetries_are_commuting_involutions_of_the_56_generating_Z2_to_the_6_preserving_X_and_commuting_with_O
  computed  PASS H3_the_63_compact_e7_generators_carry_each_nontrivial_hexagram_once_the_70_all_64_the_56_twenty_eight_twice
  computed  PASS H4_the_fermion_lifts_commute_or_anticommute_in_exactly_the_Pauli_pattern
  computed  PASS H5_A13_and_the_cycle_permute_the_plane_lines_as_GL2_F2_and_fix_the_charge_line
  argument  ARG  reading
  argument  ARG  A13_and_charge_conjugation
  argument  ARG  fence
VERDICT six symmetries of the registered gauging — two gauge-torus sign patterns, the KK ℤ₂ half-turn of the centre Z, two gauge Weyl plane swaps and C56 — form a three-qubit Pauli frame: on the bosons a ℤ₂⁶ commuting with O, under which the 63 compact e7 generators carry each non-trivial hexagram exactly once (the 70 all 64, the 56 only 28). A13 and the cycle permute the plane lines as GL(2, F₂). Junkyard tier.
RESULT_HASH 4fbefbdc65bf2832
s1264: 5 computed, 5 receipt, 3 argument, 0 failed
