s1263 — the I Ching check: the hexagram group on the 56, and on the toy fermion 64
  T_bridge_class         {"O² − I": "<1e-12", "OᵀΩO + Ω": "<1e-12", "tr O": 0.0, "fraction of grade g sent to −g": {"D56 ±2": 1.0, "D56 ±6": 1.0, "D_sol ±2": 1.0, "D_sol ±6": 1.0}, "s106l": {"a_F4_2rank_is_5": 5, "b_T_is_antisymplectic": 0.0, "c_rank_is_6": 6, "c_order_is_64": 64}}
  hexagram_group_on_56   {"Qb unitary": "<1e-12", "commute with Θ (max)": "<1e-12", "det (max |det − 1|)": "<1e-12", "involutions on the 56 (max)": "<1e-12", "commute on the 56 (max)": "<1e-12", "symplectic s1 s2 s3 Ui Uj (max)": "<1e-12", "O anti-symplectic": "<1e-12", "s4 = s1 s2 s3 on the 56": "<1e-12", "coincident pairs among the 64 products": 0}
  census_56              {"distinct characters": 50, "multiplicity profile {multiplicity: count}": {"1": 48, "4": 2}, "total dimension": 56, "line order (bit = 1 means +1)": ["s1", "s2", "s3", "Ui", "Uj", "O"], "four-fold patterns (labelling-dependent)": ["111110", "111111"], "absent patterns (labelling-dependent)": ["000000", "000001", "000010", "000011", "000100", "000101", "000110", "000111", "111000", "111001", "111010", "111011", "111100", "111101"]}
  toy                    {"P − lane toy_Parity": "<1e-12", "rank V64": 64, "Γ_y² + I": "<1e-12", "tr Γ_y": 0.0, "dim of the Θ-commutant in u(8)": 36, "max |tr_V64(U⊗1) − 4·tr U| (3 random group elements)": "<1e-09"}
  fermion_64             {"s_k ⊗ 1 involutions, commuting (max)": "<1e-12", "joint characters of ⟨s_k⟩ on V64": {"111": 16, "110": 16, "101": 16, "011": 16}, "U_i⊗1 squared + I": "<1e-12", "U_j⊗1 squared + I": "<1e-12", "Θ_ℝ⊗1 squared + I": "<1e-12", "U_i U_j + U_j U_i on V64": "<1e-12"}
  receipt   PASS filed_d1414_house_frames_npz
  receipt   PASS filed_chatgpt_d1414_maps_npz
  receipt   PASS s106l_is_the_filed_T_bridge_kernel
  receipt   PASS s106l_json_holds_the_rank6_count
  receipt   PASS p8_junkyard_holds_the_trigram_curio
  computed  PASS I1_O_is_an_anti_symplectic_traceless_involution_swapping_the_shells_the_S106_T_bridge_class
  computed  PASS I2_six_commuting_involutions_on_the_56_five_symplectic_one_anti_symplectic_generate_Z2_to_the_6
  computed  PASS I3_on_the_56_the_hexagram_group_shows_50_of_64_characters_48_once_2_four_times_14_absent
  computed  PASS I4_the_toy_parity_is_rebuilt_V64_has_rank_64_and_is_four_copies_of_the_realified_8_for_internal_operators
  computed  PASS I5_on_the_toy_64_the_lift_is_a_double_cover_O_Ui_Uj_square_to_minus1_Ui_Uj_anticommute_and_only_4_characters_of_dimension_16
  argument  ARG  reading
  argument  ARG  fence
VERDICT an S106-shaped ℤ₂⁶ (five symplectic flips + the anti-symplectic end flip) acts genuinely on the 56 and shows 50 of its 64 characters (48 once, 2 four times, 14 absent); on the toy's 64-dimensional fermion zero-mode space it lifts only to a double cover, and any genuine internal ℤ₂-action there shows at most 4 characters. The toy's 64 is not the hexagram 64.
RESULT_HASH 2fc27ed3027092f5
s1263: 5 computed, 5 receipt, 2 argument, 0 failed
