s1262 — house checks of A1774: full X, halves, parents, anchors, ladder table, declared toy, A861 metrics
  full_X                 {"Σ A_MᵀA_M − 12 I": "<1e-12", "common fixed dim": 0, "gauge algebra (dim, derived, Killing inertia)": [28, 28, [12, 16, 0]], "closure residual": "<1e-12", "rank of the e7 derivative map": 105, "max |⟨der(E_a, X), X⟩|": "<1e-10", "lane CSS basis (dim, derived, Killing)": [13, 12, [0, 1, 12]], "lane CSS basis common fixed dim": 16}
  halves                 {"D56": {"fractions": {"-6": 0.125, "-2": 0.375, "2": 0.375, "6": 0.125}, "sum − X": "<1e-12", "house pieces − lane pieces": "<1e-10", "halves": {"−": {"closure": "<1e-12", "algebra": [28, 27, [0, 16, 12]], "common fixed dim": 1}, "+": {"closure": "<1e-12", "algebra": [28, 27, [0, 16, 12]], "common fixed dim": 1}}}, "D_sol": {"fractions": {"-6": 0.125, "-2": 0.375, "2": 0.375, "6": 0.125}, "sum − X": "<1e-12", "house pieces − lane pieces": "<1e-10", "halves": {"−": {"closure": "<1e-12", "algebra": [28, 27, [8, 8, 12]], "common fixed dim": 1}, "+": {"closure": "<1e-12", "algebra": [28, 27, [8, 8, 12]], "common fixed dim": 1}}}}
  parents                {"D56 -2": {"closure": "<1e-12", "algebra": [15, 15, [0, 15, 0]]}, "D56 2": {"closure": "<1e-12", "algebra": [15, 15, [0, 15, 0]]}, "D_sol -2": {"closure": "<1e-12", "algebra": [15, 15, [8, 7, 0]]}, "D_sol 2": {"closure": "<1e-12", "algebra": [15, 15, [8, 7, 0]]}, "‖R·X − X‖/‖X‖": 1.414213562}
  anchors                {"compact gauge dim": 16, "D56": {"antisymmetric": "<1e-12", "[A, Z]": "<1e-12", "Z coefficient": -0.707106781, "residual off Z": 0.0, "tr A²": -12.0, "max |Re eig|": "<1e-12", "imag spectrum counts": {"0": 32, "+1/√2": 12, "−1/√2": 12}, "compact-gauge centralizer dim": 16, "order-two element: tr, square − I": [8.0, "<1e-10"]}, "D_sol": {"antisymmetric": "<1e-12", "[A, Z]": "<1e-12", "Z coefficient": 0.0, "residual off Z": 1.0, "tr A²": -12.0, "max |Re eig|": "<1e-12", "imag spectrum counts": {"0": 32, "+1/√2": 12, "−1/√2": 12}, "compact-gauge centralizer dim": 8, "order-two element: tr, square − I": [8.0, "<1e-10"]}}
  ladder_X_preservation  {"B1": 0.612372436, "B2": 0.612372436, "G": 0.612372436, "W_h": 2.979093822, "G2": 0.935414347, "O": 0.0, "C56": 0.0, "golden": 0.363271264}
  toy                    {"Parity² − I": "<1e-10", "projector idempotent": "<1e-10", "rank (real)": 64, "Parity on image − 1": "<1e-10", "chirality on image: square − I": "<1e-09", "chirality trace on image": 0.0, "|Im trace|": "<1e-09"}
  A861                   {"1": {"house FD vs lane G, H (rel)": ["<1e-05", "<1e-05"], "min G⁻¹H": 1.381966011, "min G·H": 0.527864045, "G·H blocks (past, present, future)": [4.0, 8.0, 16.94427191], "negative subspaces of G and H coincide": "<1e-09", "G⁻¹H past / future": 1.618033989}, "2": {"house FD vs lane G, H (rel)": ["<1e-05", "<1e-05"], "min G⁻¹H": 1.145898034, "min G·H": 0.16718427, "G·H blocks (past, present, future)": [2.11145618, 8.0, 37.88854382], "negative subspaces of G and H coincide": "<1e-09", "G⁻¹H past / future": 2.618033989}, "3": {"house FD vs lane G, H (rel)": ["<1e-05", "<1e-05"], "min G⁻¹H": 1.05572809, "min G·H": 0.05883371, "G·H blocks (past, present, future)": [1.16718427, 8.0, 88.72135955], "negative subspaces of G and H coincide": "<1e-09", "G⁻¹H past / future": 4.236067977}}
  receipt   PASS filed_d1414_house_frames_npz
  receipt   PASS filed_chatgpt_d1414_maps_npz
  receipt   PASS the_lane_program_is_the_filed_one
  receipt   PASS the_lane_report_is_the_graded_object
  receipt   PASS the_A861_drill_is_the_filed_one
  computed  PASS Q1_full_X_fixes_no_vector_has_no_rescaling_generator_and_is_so62_with_Killing_12_16
  computed  PASS Q1b_the_lane_CSS_comparison_basis_has_dim13_derived12_Killing_0_1_12_and_fixes_16
  computed  PASS Q2_each_oriented_half_closes_has_rank28_fixes_one_vector_Killing_0_16_12_D56_and_8_8_12_Dsol
  computed  PASS Q3_the_5D_parents_close_with_rank15_so6_for_D56_and_so42_for_Dsol_and_R_moves_X
  computed  PASS Q4_D56_anchor_is_minus_Z_over_root2_Dsol_anchor_is_a_noncentral_compact_rotation_centralizers_16_and_8
  computed  PASS Q5_no_ladder_element_preserves_X_and_O_C56_do_matching_the_lane_table
  computed  PASS Q6_the_declared_toy_parity_squares_to_I_and_its_constant_mode_image_is_real_64_split_evenly_by_chirality
  computed  PASS Q7_the_lane_A861_G_H_equal_the_drill_FD_both_operators_positive_negative_subspaces_coincide
  argument  ARG  what_it_closes
  argument  ARG  names_and_ladders
  argument  ARG  A861_scope
VERDICT A1774 house-checked: full X is so(6,2), fixes no vector of the 56 and has no rescaling generator — not CSS, not a single-orientation twisted reduction; each oriented half is a valid parent-plus-twist (parents so(6) for D56, so(4,2) for D_sol); the D56 anchor is −Z/√2, the D_sol anchor a non-central rotation; no ladder element preserves X; the declared toy is vectorlike; the A861 G, H match the drill and both G⁻¹H and G·H are positive with 12 negative-norm directions.
RESULT_HASH 76b1cc675a206423
s1262: 8 computed, 5 receipt, 3 argument, 0 failed
