s1259 — house checks of A1773: identification of X, quadratic spectrum, quartics, split-preserving witness, compact invariants, torus stabilizer, chirality table, A13 / C56
  identification     {"‖X‖² lane / house": [672.0, 672.0], "spec tr(X_M X_P) lane": [[-24.0, 16], [0.0, 28], [24.0, 12]], "spec max |lane − house|": "<1e-12", "70-scalar Hessian lane (s1250 frame)": [[0.0, 48], [0.166667, 20], [0.666667, 2]], "70-scalar Hessian house (s640 frame)": [[0.0, 48], [0.166667, 20], [0.666667, 2]], "70 max |lane − house|": "<1e-12", "V(o) lane / house": ["<1e-12", "<1e-12"], "grad70 lane / house": ["<1e-12", "<1e-12"], "rank span{X_M}": 28, "rank span{X_M} ∪ gauge_all28": 28, "C56 / A13 preserve X (relative)": {"C56": "<1e-12", "A13": "<1e-12"}}
  quadratic          {"Gram − I": "<1e-12", "symmetry": "<1e-12", "grad16": "<1e-12", "Hessian16": [[0.0, 6], [0.166667, 8], [0.666667, 2]], "12 × Hessian16": [[0.0, 6], [2.0, 8], [8.0, 2]], "house H16 − lane Hessian16": "<1e-10", "FD vs analytic (3 diagonal entries)": "<1e-05"}
  quartic            {"zero_quadratic_positive56": {"‖S‖_F": 1.0, "symmetry": "<1e-12", "outside noncompact span": "<1e-12", "Sᵀ H S": "<1e-10", "max |odd part| / t³": "<1e-06", "fit t² / t⁴": ["<1e-08", 0.0034722], "expected t⁴": 0.0034722}, "zero_quadratic_negative56": {"‖S‖_F": 1.0, "symmetry": "<1e-12", "outside noncompact span": "<1e-12", "Sᵀ H S": "<1e-10", "max |odd part| / t³": "<1e-06", "fit t² / t⁴": ["<1e-08", -0.0011574], "expected t⁴": -0.0011574}}
  witness            {"‖S‖_F": 1.0, "symmetry": "<1e-12", "outside house noncompact span": "<1e-12", "S56·BV − BV·S8": "<1e-12", "[S8, P_U]": "<1e-12", "G(U, U⊥)": "<1e-12", "V''(0) analytic": 0.078228361, "V(exp(0.2S)·o)": 0.001566306}
  compact_invariants {"BVᵀBV − 2I": "<1e-12", "G8² − I/4": "<1e-12", "frame": {"λ": [0.0, 0.0, 0.0, 1.0], "spec(G|U) + 1/2 − λ": "<1e-12"}, "random": {"λ": [0.00880036, 0.093911356, 0.305854361, 0.924043257], "spec(G|U) + 1/2 − λ": "<1e-12"}}
  stabilizer         {"rank of the X-variation over the 12 compact generators": 8, "fixed-X compact stabilizer dim": 4, "max ‖T_i·X‖": "<1e-12", "rank [compact ; T]": 12}
  chirality          {"Γ₈ on S₊ / S₋": [1, -1], "frame": {"G-signs U / U⊥": [[1, -1, -1, -1], [1, 1, 1, -1]], "ω_U² + I": "<1e-12", "ω_W² + I": "<1e-12", "ω_Uω_W = r·Γ₈, |r|": 1.0, "residual": "<1e-11", "table (χ_U χ_W)": {"S+": {"++": 4, "+−": 0, "−+": 0, "−−": 4}, "S-": {"++": 0, "+−": 4, "−+": 4, "−−": 0}}, "real commutant dim": {"S+": 2, "S-": 2}}, "random": {"G-signs U / U⊥": [[1, -1, -1, -1], [1, 1, 1, -1]], "ω_U² + I": "<1e-12", "ω_W² + I": "<1e-12", "ω_Uω_W = r·Γ₈, |r|": 1.0, "residual": "<1e-11", "table (χ_U χ_W)": {"S+": {"++": 4, "+−": 0, "−+": 0, "−−": 4}, "S-": {"++": 0, "+−": 4, "−+": 4, "−−": 0}}, "real commutant dim": {"S+": 2, "S-": 2}}, "control: random real complex structure on ℝ⁸, +1 eigenspace of iJ": 4}
  discrete           {"A13 L A13⁻¹ L − I": "<1e-12", "C56 L C56⁻¹ − L": "<1e-12", "L² − I (L is not an involution)": "1.618"}
  receipt   PASS filed_d1413_house_frames_npz
  receipt   PASS filed_d1412_house_frames_npz
  receipt   PASS filed_d1410_solder_npz
  receipt   PASS filed_d1409_generators_npz
  receipt   PASS filed_chatgpt_d1413_maps_npz
  receipt   PASS filed__s640_frame_npz
  receipt   PASS the_lane_program_is_the_filed_one
  receipt   PASS the_lane_report_is_the_graded_object
  computed  PASS N1_lane_X_and_house_XT_have_equal_norm_and_tr_XX_spectrum
  computed  PASS N1_the_70_scalar_Hessian_spectra_at_o_agree_across_the_s640_and_s1250_frames
  computed  PASS N1_lane_X_spans_exactly_the_house_gauge_algebra_at_o
  computed  PASS N1_C56_and_A13_preserve_X
  computed  PASS N2_the_house_noncompact_basis_is_Frobenius_orthonormal_and_symmetric
  computed  PASS N2_Hessian_on_the_16_noncompact_directions_is_0x6_one_sixth_x8_two_thirds_x2
  computed  PASS N2_the_lane_Hessian16_equals_the_house_one_in_the_shared_basis
  computed  PASS N2_finite_differences_agree_with_the_analytic_quadratic_form
  computed  PASS N3_quartic_on_zero_quadratic_positive56
  computed  PASS N3_quartic_on_zero_quadratic_negative56
  computed  PASS N4_the_witness_is_a_unit_symmetric_noncompact_so44_boost_fixing_the_frame_split
  computed  PASS N4_the_witness_changes_the_tree_potential
  computed  PASS N5_the_compact_invariants_lambda_of_both_splits
  computed  PASS N6_the_fixed_X_subalgebra_of_the_compact_so4_so4_is_the_4_torus
  computed  PASS N7_the_Spin_U_chirality_table_on_both_splits
  computed  PASS N7_control_any_real_complex_structure_on_R8_splits_4_4
  argument  ARG  N7_the_table_is_forced_house_finding_S385_6
  computed  PASS N8_A13_inverts_the_golden_boost_and_C56_commutes_with_it
  argument  ARG  scope
VERDICT A1773 house-checked: the lane's X is the house gauging (frame-free: ‖X‖² 672, tr XX spectrum and the 70-scalar Hessian equal across frames); along the 16 noncompact so(4,4) directions at o the Hessian is 0 ×6, 1/6 ×8, 2/3 ×2 with quartics +1/288 and −1/864 on the zero sector; a split-preserving boost moves V; λ(frame) = (0,0,0,1), λ(random) as printed; the fixed-X compact stabilizer is the torus; A13 inverts the golden boost; the Spin(U) chirality table holds on both splits and is forced by algebra.
RESULT_HASH ba025a17aaed6f06
s1259: 17 computed, 8 receipt, 2 argument, 0 failed
