s1267 — house checks of A1775: group table, census, Dehn sl(2), pencil, Z ~ r in the D_sol level-zero group, gauge nilpotents, golden control
  Q1_group_table       {"table": {"B1": {"order (≤12)": null, "radius": 1.0, "symplectic": "+", "frame invariance ‖MF − FK‖": "<1e-10", "K − (factor ⊗ mult)": "<1e-10", "H1 (trace, det)": [2.0, 1.0]}, "B2": {"order (≤12)": null, "radius": 1.0, "symplectic": "+", "frame invariance ‖MF − FK‖": "<1e-10", "K − (factor ⊗ mult)": "<1e-10", "H1 (trace, det)": [2.0, 1.0]}, "B1B2": {"order (≤12)": 6, "radius": 1.0, "symplectic": "+", "frame invariance ‖MF − FK‖": "<1e-10", "K − (factor ⊗ mult)": "<1e-10", "H1 (trace, det)": [1.0, 1.0]}, "B1B2B1": {"order (≤12)": 4, "radius": 1.0, "symplectic": "+", "frame invariance ‖MF − FK‖": "<1e-10", "K − (factor ⊗ mult)": "<1e-10", "H1 (trace, det)": [0.0, 1.0]}, "B1B2inv": {"order (≤12)": null, "radius": 2.618034, "symplectic": "+", "frame invariance ‖MF − FK‖": "<1e-10", "K − (factor ⊗ mult)": "<1e-10", "H1 (trace, det)": [3.0, 1.0]}, "W_h": {"order (≤12)": null, "radius": 2.618034, "symplectic": "+", "frame invariance ‖MF − FK‖": "<1e-10", "active trace / 12": 3.0}, "G": {"order (≤12)": null, "radius": 1.618034, "symplectic": "−", "frame invariance ‖MF − FK‖": "<1e-10", "K − (factor ⊗ mult)": "<1e-10", "H1 (trace, det)": [1.0, -1.0]}, "O": {"order (≤12)": 2, "radius": 1.0, "symplectic": "−", "frame invariance ‖MF − FK‖": "<1e-10", "K − (factor ⊗ mult)": "<1e-10", "H1 (trace, det)": [0.0, -1.0]}, "C56": {"order (≤12)": 2, "radius": 1.0, "symplectic": "+", "frame invariance ‖MF − FK‖": "<1e-10", "K − (factor ⊗ mult)": "<1e-10", "H1 (trace, det)": [0.0, -1.0]}, "CP": {"order (≤12)": 2, "radius": 1.0, "symplectic": "−", "frame invariance ‖MF − FK‖": "<1e-10"}}, "M_O M_C + M_C M_O": "<1e-10", "O·C56 − C56·O on the 56": "<1e-10", "O₂C₂ + C₂O₂": "<1e-12", "(C₂O₂)² + I": "<1e-12", "CP² − I on the 56": "<1e-10", "M_O² − I, M_C² − I": ["<1e-10", "<1e-10"], "B1B2 active: (M² − M + I)P_act": "<1e-10", "W_h active: (M² − 3M + I)P_act": "<1e-09"}
  Q2_census            {"words": 1456, "lock": "7278fd639272cbbb", "house vs lane class56 disagreements": 0, "lane rows": 1456, "totals": {"hyperbolic": 772, "periodic": 344, "unipotent-type": 340}, "unipotent-type with H1 trace −2": 168, "least hyperbolic radius": 2.618033989}
  Q3_dehn_sl2          {"e − (B1 − I), f − (I − B2)": ["<1e-12", "<1e-12"], "h − [e,f], r − (e − f)": ["<1e-12", "<1e-12"], "[h,e] − 2e, [h,f] + 2f": ["<1e-12", "<1e-12"], "e², f²": ["<1e-12", "<1e-12"], "e7-span residuals e, f, h, r": ["<1e-10", "<1e-10", "<1e-10", "<1e-10"], "[D_sol, ·] for e, f, h, r": ["<1e-12", "<1e-12", "<1e-12", "<1e-12"], "[D56, e] max": 4.0, "X-variation e, f": [0.5, 0.5], "centraliser (dim, Tr₅₆ inertia)": {"e": [99, [36, 30, 33]], "h": [67, [37, 30, 0]], "r": [67, [36, 31, 0]], "Z": [67, [36, 31, 0]]}, "e power ranks": [12, 0], "exp(πr) − (I − 2P_act)": "<1e-10", "spec r: |Im| counts": {"1.0": 24, "0.0": 32}}
  Q4_pencil            {"r² + P_act": "<1e-12", "S² − P_act": "<1e-12", "rS + Sr": "<1e-12", "k(π/4) − √2 e": "<1e-12"}
  Q5_conjugator        {"L in e7 (span residual)": "<1e-10", "[L, D_sol]": "<1e-12", "[L, D56] max": 4.0, "house exp − lane conjugator": "<1e-10", "gZg⁻¹ − r": "<1e-10", "gᵀΩg − Ω": "<1e-10", "‖g·X − X‖/‖X‖": 1.0, "‖Z − r‖_F, ‖[Z, r]‖_F": [6.92820323, 4.898979486]}
  Q6_gauge_nilpotents  {"P, Q in gauge span": ["<1e-10", "<1e-10"], "[Z,P] − Q, [Z,Q] + P, [P,Q] + Z": ["<1e-12", "<1e-12", "<1e-12"], "Tr₅₆ on (Z, P, Q)": [[-24.0, 0.0, 0.0], [0.0, 24.0, 0.0], [0.0, 0.0, 24.0]], "n − (Z + P)": "<1e-12", "n power ranks": [24, 12, 0], "X-variation n": "<1e-12", "centraliser n": [67, [20, 15, 32]], "four gauge representatives": {"2A1": {"in gauge span": "<1e-10", "X-variation": "<1e-12", "power ranks": [20, 2, 0], "centraliser": [81, [22, 17, 42]]}, "A2": {"in gauge span": "<1e-10", "X-variation": "<1e-12", "power ranks": [24, 12, 0], "centraliser": [67, [20, 15, 32]]}, "2A2": {"in gauge span": "<1e-10", "X-variation": "<1e-12", "power ranks": [36, 20, 4, 2, 0], "centraliser": [49, [10, 7, 32]]}, "A4": {"in gauge span": "<1e-10", "X-variation": "<1e-12", "power ranks": [40, 30, 20, 12, 4, 2, 0], "centraliser": [33, [6, 3, 24]]}}, "signed-partition enumeration, so(6,2), nonzero": ["5111", "3311", "311111", "221111"], "e power ranks vs the four": [[12, 0], [20, 2, 0], [24, 12, 0], [36, 20, 4, 2, 0], [40, 30, 20, 12, 4, 2, 0]]}
  Q7_golden_control    {"X-variation": 0.707106781, "[Y,h], [Y,Z]": ["<1e-12", "<1e-12"], "‖[Y,e]‖_F, ‖[Y,r]‖_F": [1.732050808, 2.449489743], "spectrum (real parts)": [[-1.0, 2], [-0.5, 16], [0.0, 20], [0.5, 16], [1.0, 2]], "max |Im eig|": "<1e-09", "centraliser": [49, [28, 21, 0]]}
  receipt   PASS filed_d1414_house_frames_npz
  receipt   PASS filed_chatgpt_d1415_maps_npz
  receipt   PASS the_lane_program_is_the_filed_one
  receipt   PASS the_lane_output_is_the_graded_object
  receipt   PASS the_lane_report_is_the_graded_object
  receipt   PASS the_lane_word_census_is_the_filed_one
  computed  PASS Q1_group_table_reproduced_and_O_C56_extend_only_separately_their_2x2_factors_anticommute
  computed  PASS Q2_the_1456_word_census_agrees_word_by_word_340_344_772_with_168_negative_unipotent
  computed  PASS Q3_the_dehn_sl2_is_e_f_from_B1_B2_level_zero_for_Dsol_not_gauge_e_centraliser_99_orbit_34
  computed  PASS Q4_r2_minus_P_S2_P_anticommute_and_the_wall_is_root2_e
  computed  PASS Q5_Z_and_r_are_conjugate_by_an_exhibited_element_of_the_connected_Dsol_level_zero_group_which_moves_X
  computed  PASS Q6_gauge_so21_null_n_in_A2_orbit_four_gauge_nilpotent_classes_and_the_dehn_orbit_absent
  computed  PASS Q7_golden_generator_not_gauge_commutes_with_h_and_Z_not_e_r_centraliser_49
  argument  ARG  completeness_is_the_lane_argument
  argument  ARG  what_it_closes
  argument  ARG  typing_corrections
VERDICT A1775 house-checked: the group table and the 1456-word census reproduce word by word; O and C56 extend the homology functor only separately; e, f are B1 − I, I − B2, level zero for D_sol, not gauge, centraliser 99 (orbit 34); Z ~ r by an exhibited element of the connected D_sol level-zero group that moves X; the gauge so(6,2) meets exactly four nonzero nilpotent classes, none of them e's; the golden generator commutes with h and Z only.
RESULT_HASH 66d49d3dccd1fb5b
s1267: 7 computed, 6 receipt, 3 argument, 0 failed
