s1307 — house checks of A1785 (D1423)
  Q0_receipt_trace               {"tr(B1 @ B2)": 44, "distance of tr(B1 @ B2) to that integer": "<1e-10"}
  Q1_A2_kernel_centre_section    {"d² − z, d⁴ − I": ["<1e-12", "<1e-12"], "[d, B1], [d, B2]": ["<1e-12", "<1e-12"], "O d O⁻¹ − d⁻¹, C d C⁻¹ − d⁻¹": ["<1e-12", "<1e-12"], "NONCENTRAL: |O d − d O|; d ≠ ±I: |d − I|, |d + I|": [2.0, 1.0, 1.0], "z² − I, tr z, [z, O], [z, C]": ["<1e-12", 8, "<1e-12", "<1e-12"], "section: s² − I, r³ − I, o² − I": ["<1e-12", "<1e-12", "<1e-12"], "section: o s o − s, o r o − r⁻¹": ["<1e-12", "<1e-12"]}
  Q2_A1c_fusion_obstruction      {"G − B1·O": "<1e-12", "rank(G² − G − I) on the 56": 44, "dim of the common fixed space of B1, B2": 32, "Γ-stability of that space (O, C56 leak)": ["<1e-12", "<1e-12"], "on it: O² − I, C56² − I, [O, C56]": ["<1e-12", "<1e-12", "<1e-12"]}
  Q3_A1_exact                    {"V₁Vₙ = Vₙ₊₁ + Vₙ₋₁ classes in ℤ[τ]/(τ² − τ − 1)": ["1", "x", "x", "1", "0", "-1"], "F_G² − F_G − I": "[0, 0, 0, 0]", "swap·F_G·swap − N_τ": "[0, 0, 0, 0]", "‖R − R⁻¹‖_F − √5": "<1e-12", "R¹⁰ − I, F² − I": ["<1e-12", "<1e-12"]}
  Q4_B1                          {"Wh_56x56 − W_h": "<1e-12", "H_φ² − W_h": "<1e-12", "P² − P, rank P": ["<1e-12", 24], "H_φ − ((I − P) + (W_h − I + 2P)/√5)": "<1e-12", "tr H_φ − (32 + 12√5)": "<1e-10", "R_Γ = B1B2⁻¹C56: R_Γ² − W_h, symplectic defect, tr": ["<1e-12", "<1e-12", -8], "G² − B1B2⁻¹, B1G²B1⁻¹ − W_h, G anti-symplectic": ["<1e-12", "<1e-12", "<1e-12"], "W_h − Λ²-lift(W₈)": "<1e-12", "R₈: det, R₈² − W₈": [1, "<1e-15"], "R₅₆: distance to ℤ, symplectic defect, normalises e7 (residual), R₅₆² − W_h, tr": ["<1e-15", "<1e-12", "<1e-10", "<1e-12", 8]}
  Q5_B2_lattices                 {"number of lattice bases": 17, "Q: orthogonal, symplectic, normalises e7": ["<1e-12", "<1e-12", "<1e-10"], "Q commutes with B1, B2, O": ["<1e-12", "<1e-12", "<1e-12"], "Q⁻¹ C56 Q: distance to ℤ": "<1e-12", "lattice_bases[r] − Q·T_r (max over r)": "<1e-12", "max over r and the four generators: distance of L⁻¹XL to ℤ": "<1e-10", "Ω-Gram: max distance to ℤ, set of determinants": ["<1e-10", [1]]}
  Q6_B2c_Lie_order               {"e7_basis: distance to ℤ": "<1e-12", "all 8778 brackets: max distance of 2·(coordinates) to ℤ": "<1e-09", "max over a, r: distance of 8·L_r⁻¹(Q E_a Q⁻¹)L_r to ℤ": "<1e-09", "CONTROL: without the factor 8 on Λ₁₆ the distance is ≥ 0.1": true}
  Q7_B2d_ranks                   {"braid-fixed coordinates are exactly the shipped 32 indices in every basis": true, "rank_F2(O − I) on Λ_r ∩ V_triv, r = 0..16": [16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]}
  receipt   PASS filed_d1414_house_frames_npz
  receipt   PASS filed_D1200_A1512_ARTIFACTS_npz
  receipt   PASS filed_chatgpt_d1416_intertwiners_npz
  receipt   PASS filed_chatgpt_d1423_maps_npz
  receipt   PASS lane_program_chatgpt_d1423_two_legs_py_NOT_IMPORTED
  receipt   PASS lane_return_manifest
  receipt   PASS as_sent_D1423_md_inside_the_return
  computed  PASS Q0_tr_B1_B2_is_44_as_the_lane_echoed
  computed  PASS Q1_A2_d_is_an_order_4_element_commuting_with_the_braids_inverted_by_O_and_C_hence_noncentral_with_d2_the_centre_z_and_the_lane_section_satisfies_the_PGL2Z_presentation
  computed  PASS Q2_A1c_rank_G2_minus_G_minus_I_is_44_and_the_32_dim_braid_fixed_sector_is_Gamma_stable_with_commuting_involutions_so_no_element_of_Gamma_satisfies_the_fusion_polynomial
  symbolic  PASS Q3_A1b_resultant_of_the_homology_and_Fibonacci_W_h_polynomials_is_phi_to_the_4
  computed  PASS Q3_A1_the_recurrence_gives_1_tau_tau_1_0_minus1_the_module_identities_hold_and_the_mirror_collapse_is_sqrt5
  computed  PASS Q4_B1_H_phi_squared_equals_W_h_by_the_lane_formula_and_both_nonprincipal_integral_symplectic_roots_square_to_W_h
  computed  PASS Q5_B2_seventeen_bases_Q_T_r_on_which_B1_B2_O_C56_act_integrally_and_the_Omega_Gram_is_integral_unimodular
  computed  PASS Q6_B2c_the_e7_basis_is_integral_its_brackets_are_half_integral_and_eight_times_the_rotated_basis_acts_integrally_on_all_seventeen_lattices
  computed  PASS Q7_B2d_the_F2_ranks_are_16_minus_r_seventeen_distinct_values
  argument  ARG  reading
  argument  ARG  scope
VERDICT: the A1785 return reproduces in house on every rebuilt identity: H_φ² = W_h exactly; a noncentral C₄ kernel with a split section over PGL(2, ℤ); integral symplectic square roots of W_h; seventeen unimodular Γ-lattices with an integral ×8 Lie order and F₂-ranks 16 − r; rank(G² − G − I) = 44; resultant φ⁴.
RESULT_HASH 6c332aff0500c358
s1307: 8 computed, 1 symbolic, 7 receipt, 2 argument, 0 failed
