s1287 — house checks of A1778
  Q1_factor_objects                    {"A (lane) − A (house archive)": "<1e-12", "U − [A,[A,D56]]/8": "<1e-12", "U − house ûₖ = D56ₖ/2": "<1e-12", "[A,U] − 2K, [K,U] − 2A, [K,A] + 2U": "<1e-12", "‖A‖², ‖U‖²": [24.0, 24.0]}
  Q2_golden_correction                 {"k: orthogonal, symplectic, k·X − X, kZkᵀ − Z": ["<1e-12", "<1e-12", "<1e-12", "<1e-12"], "Ad(k)(U₁ − U₂)/2 − Y_g": "<1e-12", "‖U₁ − U₂‖², ‖Y_g‖²": [48.0, 12.0]}
  Q3_D56_face_CSS_map                  {"g − exp(πK/2) (house K)": "<1e-12", "g normalises e7 (max residual); gᵀΩg − Ω": ["<1e-12", "<1e-12"], "gD56g⁻¹ + D56": "<1e-12", "actX(g, Θ) − house face(+D56)": "<1e-12", "house face(+D56)[55] + Z/√2": "<1e-12", "Θ from its 133 coefficients": "<1e-12", "Θ shape": {"first-index support (dim)": 28, "support isotropic": "<1e-12", "D56 weights": [-6.0], "singlet M = Θ[27]: antisymmetric, commutes with D56, in e7": ["<1e-12", "<1e-12", "<1e-12"], "the other 27 generators: max ‖N³‖": "<1e-12"}}
  Q4_other_CSS_maps                    {"F1": {"g in E7 (normaliser residual, symplectic)": ["<1e-12", "<1e-12"], "actX(g, Θ) − house face": "<1e-12", "Θ shape": {"first-index support (dim)": 28, "support isotropic": "<1e-12", "D56 weights": [-6.0], "singlet M = Θ[27]: antisymmetric, commutes with D56, in e7": ["<1e-12", "<1e-12", "<1e-12"], "the other 27 generators: max ‖N³‖": "<1e-12"}}, "E01": {"g in E7 (normaliser residual, symplectic)": ["<1e-12", "<1e-12"], "actX(g, Θ) − house face": "<1e-12", "Θ shape": {"first-index support (dim)": 28, "support isotropic": "<1e-12", "D56 weights": [-6.0], "singlet M = Θ[27]: antisymmetric, commutes with D56, in e7": ["<1e-12", "<1e-12", "<1e-12"], "the other 27 generators: max ‖N³‖": "<1e-12"}}, "THREE1": {"g in E7 (normaliser residual, symplectic)": ["<1e-12", "<1e-12"], "actX(g, Θ) − house face": "<1e-12", "Θ shape": {"first-index support (dim)": 28, "support isotropic": "<1e-12", "D56 weights": [-6.0], "singlet M = Θ[27]: antisymmetric, commutes with D56, in e7": ["<1e-12", "<1e-12", "<1e-12"], "the other 27 generators: max ‖N³‖": "<1e-12"}}}
  Q5_census_reproduced                 {"rows": 57, "rows whose house (dim, derived, Killing, fixed) differs from the lane": [], "one-twist rows compared; max |overlap| difference (Z, Q₁₂)": [49, "<1e-08"], "lane CSS_shape True / False": [49, 8]}
  Q6_tower_and_fixed_vector_obstruction {"X = Σ pieces of D56 weight 6, 2, −2, −6 (residual)": "<1e-12", "e^{−6t}actX(e^{tD56}, X) − (X₆ + εX₂ + ε²X₋₂ + ε³X₋₆), t = 0.3": "<1e-12", "common fixed dims of the cumulative collections": [16, 1, 0, 0], "Σ_M (√2X_M)ᵀ(√2X_M) − 24 I": "<1e-12"}
  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_d1418_maps_npz
  receipt   PASS A1778_census_csv_graded_object
  receipt   PASS s1283_results_construction_and_machinery
  receipt   PASS s1284_results_face_and_invariant_machinery
  computed  PASS Q1_the_lane_U_and_K_are_the_house_radius_axes_and_their_sl2_partners
  computed  PASS Q2_the_golden_generator_is_Ad_k_of_HALF_the_factor_difference_the_dispatched_G5_dropped_a_factor_one_half
  computed  PASS Q3_the_lane_map_carries_a_CSS_tensor_onto_the_house_D56_face_via_the_clock_quarter_turn_and_the_singlet_gauges_minus_Z_over_root2
  computed  PASS Q4_the_four_form_generic_and_three_factor_maps_carry_CSS_tensors_onto_the_house_faces
  computed  PASS Q5_the_house_face_invariants_equal_the_lane_census_at_all_57_directions
  computed  PASS Q6_the_D56_deformation_tower_and_the_common_fixed_dimensions_16_1_0_0
  argument  ARG  reading
  argument  ARG  scope
VERDICT: A1778 confirmed on the house substrate — the lane's CSS maps carry CSS-shaped tensors onto the house faces (D56 via exp(πK/2), singlet gauging −Z/√2), its 57-row census is reproduced by the house face machinery, the golden correction (factor ½) holds, and the D56 tower and the 16, 1, 0, 0 fixed dimensions are confirmed.
RESULT_HASH 3b45ff3804fdc5e4
s1287: 6 computed, 7 receipt, 2 argument, 0 failed
