s1290 — the vacuum as an electromagnetic medium on F0
  Q1_electric_frame_and_dyonic_content   {"rank of A ↦ A^M X_M; dim K": [28, 28], "K, E Lagrangian (max |·ᵀΩ·|)": ["<1e-12", "<1e-12"], "electric/magnetic angle / π over 33 electric directions (min, max)": [0.25, 0.25], "Z field vector: residual of A^M X_M = Z, angle / π": ["<1e-12", 0.25], "T0 field vectors: residual": "<1e-12", "Z in T0 (relative residual)": "<1e-12", "HF torus T vs T0: projector difference": 0.03554}
  Q2_trivial_medium_at_o                 {"−Im𝒩(o) − I₂₈": "<1e-12", "Re𝒩(o)": "<1e-12", "symplectic consistency": "<1e-10", "ε_Z(o), θ_Z(o)": [1.0, 0.0]}
  Q3_A1765_theta_matrix                  {"[T0, M] at P08": "<1e-12", "symplectic consistency": "<1e-10", "spec K4: house, lane": [[0.594687, 1.045902, 1.138608, 1.246119], [0.594687, 1.045902, 1.138608, 1.246119]], "max |Δ spec K4|, |Δ spec θ4| (orientation sign), |Δ spec K4⁻¹θ4|": ["<1e-08", "<1e-08", "<1e-08"], "orientation sign relating the two θ conventions": -1, "gravitino masses at the house P08": [0.635511, 0.662863, 0.690029, 0.916412]}
  Q4_four_form_flat                      {"max |Re𝒩| on 28 (5 points)": "<1e-12", "max |ε_Z − ¼Σᵢexp(−2χᵢ·s)| and consistency": "<1e-12"}
  Q5_radius_flat_and_D56_edge            {"max |𝒩_Z − (tanh 2Σs − i sech 2Σs)| (5 points)": "<1e-12", "D56 ray: ε_Z, sech 12a, θ_Z, tanh 12a": {"a = 0.1": [0.552286, 0.552286, 0.833655, 0.833655], "a = 0.25": [0.099328, 0.099328, 0.995055, 0.995055], "a = 0.5": [0.004957, 0.004957, 0.999988, 0.999988]}}
  Q6_parity                              {"(ε_Z, θ_Z) at 3 generic points": [[1.070585, 0.80941], [0.930984, -0.428262], [0.90959, 0.445127]], "max |Δε|, |θ + θ′|, spectra (−Im𝒩 equal, Re𝒩 negated)": "<1e-10", "|𝒩_Z|² at the samples": [1.801297, 1.05014, 1.025492]}
  receipt   PASS filed_d1414_house_frames_npz
  receipt   PASS filed_chatgpt_d1414_maps_npz
  receipt   PASS filed_chatgpt_d1417_maps_npz
  receipt   PASS filed_chatgpt_d1405_maps_npz
  receipt   PASS s1283_results_construction_and_machinery
  receipt   PASS s1284_results_face_and_twist_definitions
  receipt   PASS s1286_results_neutral_count_machinery
  computed  PASS Q1_K_and_E_are_Lagrangian_and_every_gauge_field_is_a_45_degree_electric_magnetic_mix_in_the_SL8_frame
  computed  PASS Q2_at_o_minus_Im_N_is_the_identity_and_Re_N_vanishes_on_all_28_vectors
  computed  PASS Q3_the_house_reproduces_A1765s_kinetic_matrix_and_theta_matrix_of_the_four_massless_vectors_at_P08
  computed  PASS Q4_on_the_four_form_flat_theta_vanishes_for_all_28_and_eps_Z_is_the_mean_of_exp_minus_2_chi_s
  computed  PASS Q5_on_the_radius_flat_N_Z_is_tanh_minus_i_sech_of_twice_the_sum_and_on_the_D56_ray_eps_Z_is_sech_12a_theta_Z_tanh_12a
  computed  PASS Q6_parity_phi_to_minus_phi_keeps_the_permittivity_and_flips_theta
  argument  ARG  reading
  argument  ARG  scope
VERDICT: at o the registered vacuum is the trivial medium (ε = μ = 1, θ = 0, coupling an input); every gauge field is a 45° dyon of the SL(8) frame; A1765's θ-matrix is reproduced; off o, θ is parity-odd and absent on the four-form flat, and Z's complex coupling moves on a hyperbolic plane — on the radius flat 𝒩_Z = tanh(2Σs) − i·sech(2Σs), ε_Z → 0 at the D56 edge.
RESULT_HASH 54842841fb96065f
s1290: 6 computed, 7 receipt, 2 argument, 0 failed
