s1304 — the strip as a local system
  Q1_O_is_Omega_P                        {"compact generators (antisymmetric parts of e7)": 63, "commutant of the compact generators: dim, max |[c, k]| on all 63": [2, "<1e-12"], "Ω in that commutant (residual of projection)": "<1e-10", "Ω² + I": "<1e-12", "P² − I, PᵀΩP + Ω, [P, D56]": ["<1e-12", "<1e-12", "<1e-12"], "O − Ω·P": "<1e-12", "CONTROL O − P (P alone is not O)": "1.000e+00", "O·Ω + Ω·O (O anticommutes with J0)": "<1e-12"}
  Q2_sections_are_lagrangian             {"O symmetric, orthogonal, O² − I": ["<1e-12", "<1e-12", "<1e-12"], "dim V₊, dim V₋": [28, 28], "Ω on V₊, Ω on V₋": ["<1e-12", "<1e-12"], "rank of the Ω-pairing V₊ × V₋": 28}
  Q3_K_is_V_minus_E_is_V_plus            {"dim K, dim E": [28, 28], "Ω on K": "<1e-12", "dim K ∩ V₋, dim K ∩ V₊": [28, 0], "dim E ∩ V₊, dim E ∩ V₋": [28, 0], "max_{M ∈ K-basis} |Σ Aᴹ X_M|": "<1e-12"}
  Q4_per_level                           {"V_6 ⊕ V_−6: dim, O-leak out of the pair, #(+1), #(−1)": [2, "<1e-12", 1, 1], "V_2 ⊕ V_−2: dim, O-leak out of the pair, #(+1), #(−1)": [54, "<1e-12", 27, 27]}
  Q5_commutant_of_the_gauge_algebra      {"max |[O, g]| over the 28 gauge generators": "<1e-12", "commutant of the gauge algebra in gl(56): dim, max |[c, g]| on all 28": [4, "<1e-12"], "closed under products (associative algebra)": "<1e-10", "its symplectic part: dim, trace-form inertia (+,−,0)": [3, [2, 1, 0]], "I and O in the commutant (projection residuals)": ["<1e-10", "<1e-10"], "idempotents (I ± O)/2: square residual": "<1e-12"}
  Q6_Omega_is_a_pseudo_form              {"|Ω_even| / |Ω|, |Ω_odd − Ω| / |Ω|": ["<1e-12", "<1e-12"], "dims of O-even / O-odd antisymmetric forms on the 56 (by counting from Q2, not a gate)": [756, 784], "CONTROL: the Euclidean form δ is O-even (Oᵀ δ O − δ)": "<1e-12"}
  Q7_parities                            {"D56": "odd", "D_sol": "odd", "Z": "even", "O·X − X": "<1e-12"}
  receipt   PASS filed_d1414_house_frames_npz
  receipt   PASS s1288_results_machinery_basis_and_actX
  computed  PASS Q1_the_commutant_of_the_63_compact_generators_is_2_dim_and_contains_Omega_with_square_minus_one_and_O_equals_Omega_times_P_exactly
  computed  PASS Q2_the_periodic_and_antiperiodic_sections_are_complementary_Lagrangians_28_plus_28
  computed  PASS Q3_the_kernel_K_of_A_to_A_M_X_M_is_exactly_the_antiperiodic_Lagrangian_and_the_electric_frame_E_is_exactly_the_periodic_one
  computed  PASS Q4_O_preserves_each_level_pair_and_splits_it_evenly_1_1_and_27_27
  computed  PASS Q5_O_commutes_with_the_gauge_algebra_whose_commutant_is_a_4_dim_matrix_algebra_with_idempotents_symplectic_part_sl2R_and_O_its_anti_symplectic_reflection
  computed  PASS Q6_Omega_has_zero_O_even_part_so_on_the_mapping_torus_it_is_a_section_of_the_orientation_line_tensor_Lambda2
  computed  PASS Q7_the_gradings_D56_and_D_sol_are_O_odd_Z_is_O_even_and_X_is_O_invariant
  argument  ARG  reading
  argument  ARG  scope
VERDICT: the Möbius monodromy is the house parity O = Ω·P; its periodic sections are exactly the electric frame E of X and its antiperiodic sections exactly K, two complementary Lagrangians; O commutes with the whole gauge algebra and is the anti-symplectic reflection of its gl(2) commutant; Ω is a pseudo-form on the strip.
RESULT_HASH 1e8a6191c5b8b810
s1304: 7 computed, 2 receipt, 2 argument, 0 failed
