s1275 — gravitini, the SU(8) frame, and the Scherk–Schwarz spectrum
  Q1_su8_frame                 {"γ relation": "<1e-12", "triality homomorphism residual": {"8_s": "<1e-12", "8_c": "<1e-12"}, "compact generators": 63, "8_s: max fit residual, antihermitian, trace": ["<1e-12", "<1e-12", "<1e-12"], "8_c control: some compact generator fails to fit (max residual > 0.1)": true}
  Q2_potential_identity        {"A1 symmetric (max)": "<1e-12", "A2 traceless / antisymmetric (max)": "<1e-12", "V at the six points": {"SO(8) at o": -6.0, "registered at o": 0.0, "so(4,4) twin at o": 2.0, "registered at (0.3, 0.2)": 0.0, "SO(8) displaced": -6.00833, "registered displaced": 0.0}, "fitted (α, β) in V = α|A1|² + β|A2|²": [-0.244898, 0.666667], "fit residual": "<1e-12", "implied (Â1/A1, Â2/A2)": [0.571429, 4.0]}
  Q3_gravitini                 {"SO(8) at o": {"1.414214": 8}, "so(4,4) twin at o": {"0.0": 8}, "registered at o": {"0.707107": 8}, "SO(8): m₃/₂² vs −V/3": [2.0, 2.0]}
  Q4_scherk_schwarz_at_o       {"q_Z on 8_s": {"-0.5": 4, "0.5": 4}, "|q_Z| on p (70)": {"0.0": 36, "1.0": 32, "2.0": 2}, "|q_Z| on the gauge span (28)": {"0.0": 16, "1.0": 12}, "vector m² (nonzero)": {"2.0": 12}, "scalar m² (12 × Hessian, nonzero)": {"2.0": 20, "8.0": 2}, "gravitino m₃/₂²": 0.5, "SS check: 2q² for gravitini, massive vectors, massive scalars": [0.5, 2.0, [2.0, 8.0]], "|q_Z| on Λ³8_s": {"0.5": 48, "1.5": 8}, "raw A3 singular values / smallest (ratio pattern)": {"1.0": 40, "2.0": 8, "3.0": 8}, "STr M² with the SS-predicted spin-1/2 (scalars, −2·spin½, 3·vectors, −4·gravitini)": [56.0, -112.0, 72.0, -16.0, 0.0]}
  Q5_radius_torus              {"grid": {"(-0.25, -0.25)": {"m₃/₂²": 1.881098, "vector m²": {"2.762196": 8, "4.762196": 8, "7.524391": 4}}, "(-0.25, +0.00)": {"m₃/₂²": 1.837113, "vector m²": {"7.348452": 12}}, "(-0.25, +0.25)": {"m₃/₂²": 7.077058, "vector m²": {"10.391921": 8, "17.916312": 8, "28.308233": 4}}, "(+0.00, -0.25)": {"m₃/₂²": 1.837113, "vector m²": {"3.086161": 8, "4.262291": 8, "7.348452": 4}}, "(+0.00, +0.00)": {"m₃/₂²": 0.5, "vector m²": {"2.0": 12}}, "(+0.00, +0.25)": {"m₃/₂²": 1.837113, "vector m²": {"3.086161": 8, "4.262291": 8, "7.348452": 4}}, "(+0.25, -0.25)": {"m₃/₂²": 7.077058, "vector m²": {"10.391921": 8, "17.916312": 8, "28.308233": 4}}, "(+0.25, +0.00)": {"m₃/₂²": 1.837113, "vector m²": {"7.348452": 12}}, "(+0.25, +0.25)": {"m₃/₂²": 1.881098, "vector m²": {"2.762196": 8, "4.762196": 8, "7.524391": 4}}}, "max relative deviation from the closed forms": "<1e-09", "gravitino degeneracy (max spread)": "<1e-09", "b = 0: vector m² / m₃/₂² values": [4.0]}
  receipt   PASS filed_d1414_house_frames_npz
  receipt   PASS filed_chatgpt_d1414_maps_npz
  computed  PASS Q1_octonionic_cl8_gives_the_su8_frame_on_8s_every_compact_generator_is_su8_and_the_8c_choice_fails
  computed  PASS Q2_V_equals_minus_three_quarters_A1_squared_plus_one_24th_A2_squared_exactly_at_six_points_with_A1hat_4_7_A1_and_A2hat_4_A2
  computed  PASS Q3_so8_has_n8_with_m32L_1_so44_has_A1_zero_and_the_registered_vacuum_breaks_all_eight_with_degenerate_m32_squared_one_half
  computed  PASS Q4_at_o_every_gravitino_vector_and_scalar_mass_is_root2_times_its_Z_charge_the_scherk_schwarz_formula_with_twist_Z
  computed  PASS Q5_on_the_radius_torus_eight_degenerate_gravitini_and_the_vector_levels_follow_the_closed_forms_and_D56_scales_the_spectrum_uniformly
  argument  ARG  what_it_says
  argument  ARG  kk_angle_now
  argument  ARG  scope
VERDICT: in the octonionic SU(8) frame the T-tensor satisfies the N = 8 potential identity exactly; the registered Minkowski vacuum at o breaks all eight supersymmetries with degenerate gravitini m₃/₂² = 1/2, and its whole bosonic + gravitino spectrum is m = √2|q_Z| — a Scherk–Schwarz spectrum with twist Z (App G's centre, the photon); on the radius torus the gravitini stay degenerate (m₃/₂² = ½cosh²(4a−4b)cosh(4a+4b)), D56 scales the spectrum uniformly, D_sol moves its ratios. Tree level; spin-1/2 as a ratio pattern only.
RESULT_HASH 42123f4ff5d08b01
s1275: 5 computed, 2 receipt, 3 argument, 0 failed
