s1253 — NEXT [2]: the golden frame on the pointed shell
  pointing       {"c-isotope house − lane": "<1e-12", "idempotent identities": "<1e-12", "Σf′ − c": "<1e-12", "N(c)": 1.0, "lift(g27) − g56": "<1e-12"}
  golden         {"App E :90": "\\boxed{\\;\\vac=\\diag(\\phi,\\,1,\\,\\phi^{-1}),\\qquad \\phi=\\tfrac{1+\\sqrt5}{2}.\\;}", "N(v)": 1.0, "golden idempotents in J^(v)": "<1e-12", "U_w: J → J^(v)": "<1e-12", "U_w·1 − v": "<1e-12", "KV signature": {"1": [15, 12], "v": [15, 12], "c": [15, 12]}}
  orderings      {"cycle preserves V₋₂": "<1e-12", "[cycle, Z]": "<1e-12", "cycle orbits": [["(0, 1, 2)", "(1, 2, 0)", "(2, 0, 1)"], ["(0, 2, 1)", "(1, 0, 2)", "(2, 1, 0)"]], "A13": {"automorphism of J^(c)": "<1e-10", "fixes c": "<1e-10", "f′1↔f′3, f′2 fixed": "<1e-10", "[L,D56]": "<1e-10", "[L,Z]": "<1e-10", "gauge-normaliser": "<1e-10"}, "A13 on the projected eights (overlap matrix)": [[1.0, 0.0, 0.0], [0.0, 0.0, 1.0], [0.0, 1.0, 0.0]], "orbit of ⟨cycle, A13⟩ from (0,1,2)": ["(0, 1, 2)", "(0, 2, 1)", "(1, 0, 2)", "(1, 2, 0)", "(2, 0, 1)", "(2, 1, 0)"], "O·L(K_τ)·O⁻¹ − L(K_τ)⁻¹ (max over τ)": "<1e-10", "max placement-match residual": "<1e-12"}
  eight_grading  {"(0, 1, 2)": {"eight2": 1.27201965, "eight1": 1.0, "eight3": 0.786151378}, "(0, 2, 1)": {"eight2": 1.0, "eight1": 1.27201965, "eight3": 0.786151378}, "(1, 0, 2)": {"eight2": 1.27201965, "eight1": 0.786151378, "eight3": 1.0}, "(1, 2, 0)": {"eight2": 1.0, "eight1": 0.786151378, "eight3": 1.27201965}, "(2, 0, 1)": {"eight2": 0.786151378, "eight1": 1.27201965, "eight3": 1.0}, "(2, 1, 0)": {"eight2": 0.786151378, "eight1": 1.0, "eight3": 1.27201965}}
  vs_G           {"exp(ln φ·Y) − L(K)": "<1e-10", "Y in e7": "<1e-10", "spec Y": [[-1.0, 2], [-0.5, 16], [0.0, 20], [0.5, 16], [1.0, 2]], "spec G": [[-1.0, 12], [0.0, 32], [1.0, 12]], "CONTROL spec gGg⁻¹": [[-1.0, 12], [0.0, 32], [1.0, 12]], "tr Y²": 12.0, "tr G²": 24.0}
  placement (0, 1, 2) {"N(v_τ)": 1.0, "‖Z·B·v_τ‖": "<1e-12", "max_a ‖T_a·B·v_τ‖": "<1e-12", "symplectic": "<1e-12", "e7-normaliser": "<1e-12", "[L,D56]": "<1e-12", "[L,Z]": "<1e-12", "max_a [L,T_a]": "<1e-12", "gauge-normaliser": 0.338603462, "[L,cycle]": 0.642060309}
  placement (0, 2, 1) {"N(v_τ)": 1.0, "‖Z·B·v_τ‖": "<1e-12", "max_a ‖T_a·B·v_τ‖": "<1e-12", "symplectic": "<1e-12", "e7-normaliser": "<1e-12", "[L,D56]": "<1e-12", "[L,Z]": "<1e-12", "max_a [L,T_a]": "<1e-12", "gauge-normaliser": 0.386636189, "[L,cycle]": 0.412241441}
  placement (1, 0, 2) {"N(v_τ)": 1.0, "‖Z·B·v_τ‖": "<1e-12", "max_a ‖T_a·B·v_τ‖": "<1e-12", "symplectic": "<1e-12", "e7-normaliser": "<1e-12", "[L,D56]": "<1e-12", "[L,Z]": "<1e-12", "max_a [L,T_a]": "<1e-12", "gauge-normaliser": 0.348363081, "[L,cycle]": 0.642060309}
  placement (1, 2, 0) {"N(v_τ)": 1.0, "‖Z·B·v_τ‖": "<1e-12", "max_a ‖T_a·B·v_τ‖": "<1e-12", "symplectic": "<1e-12", "e7-normaliser": "<1e-12", "[L,D56]": "<1e-12", "[L,Z]": "<1e-12", "max_a [L,T_a]": "<1e-12", "gauge-normaliser": 0.386636189, "[L,cycle]": 0.412241441}
  placement (2, 0, 1) {"N(v_τ)": 1.0, "‖Z·B·v_τ‖": "<1e-12", "max_a ‖T_a·B·v_τ‖": "<1e-12", "symplectic": "<1e-12", "e7-normaliser": "<1e-12", "[L,D56]": "<1e-12", "[L,Z]": "<1e-12", "max_a [L,T_a]": "<1e-12", "gauge-normaliser": 0.348363081, "[L,cycle]": 0.642060309}
  placement (2, 1, 0) {"N(v_τ)": 1.0, "‖Z·B·v_τ‖": "<1e-12", "max_a ‖T_a·B·v_τ‖": "<1e-12", "symplectic": "<1e-12", "e7-normaliser": "<1e-12", "[L,D56]": "<1e-12", "[L,Z]": "<1e-12", "max_a [L,T_a]": "<1e-12", "gauge-normaliser": 0.338603462, "[L,cycle]": 0.642060309}
  receipt   PASS filed_d1410_solder_npz
  receipt   PASS filed_d1409_generators_npz
  receipt   PASS filed_chatgpt_d1410_maps_npz
  receipt   PASS filed_D1200_A1512_ARTIFACTS_npz
  receipt   PASS app_E_is_the_printed_file_whose_line_90_boxes_the_golden_frame
  computed  PASS K1_the_pointed_shell_algebra_of_A1770_is_reproduced_from_the_house_sharp_map_and_g27_lifts_to_the_lanes_g56
  computed  PASS K2_the_golden_frame_lambda_k_f_k_is_a_frame_of_the_v_isotope_U_w_is_an_isomorphism_and_the_KV_signature_is_15_12_at_1_v_and_c
  computed  PASS K3_for_all_six_orderings_the_pointed_shell_maps_onto_the_golden_frame_by_an_explicit_isotope_isomorphism
  computed  PASS K4_every_placed_golden_point_is_torus_neutral_and_its_boost_from_c_is_in_E7_commutes_with_D56_Z_and_the_torus_but_is_not_a_gauge_symmetry_nor_cycle_invariant
  computed  PASS K5_the_six_placements_are_one_orbit_of_the_registered_group_generated_by_the_plane_cycle_and_a_c_fixing_gauge_normalising_transposition_and_O_inverts_the_boost
  computed  PASS K6_the_boost_from_c_to_the_golden_point_scales_each_of_F0s_three_eights_by_sqrt_lambda_i_lambda_j_one_eight_fixed_two_reciprocal
  computed  PASS K7_the_lifted_shell_golden_generator_has_spectrum_pm1x2_pmhalf_x16_0x20_and_is_not_conjugate_to_any_multiple_of_A1769s_G_control_passes
  argument  ARG  what_NEXT_2_now_reads
  argument  ARG  scope
VERDICT A1770's pointed shell algebra and App E's golden frame are isomorphic framed isotopes for every ordering; the placed golden point is torus-neutral, its boost from c lies in E7 and commutes with D56, Z and the torus but is not a gauge symmetry; the six orderings are one orbit of the registered ⟨cycle, A13⟩ and O inverts the boost — the ordering is a loading; the boost grades the three eights by √φ, 1, 1/√φ; it is not conjugate to A1769's G.
RESULT_HASH 2b60cfa6a7a9e16d
s1253: 7 computed, 5 receipt, 2 argument, 0 failed
