s1279 — the KK angle and the golden line
  Q1_kk_angle              {"points": {"(-0.25, -0.25)": {"two single-charge vector levels (low, high), m₃/₂²": [2.762196, 4.762196, 1.881098]}, "(-0.25, +0.00)": {"two single-charge vector levels (low, high), m₃/₂²": [0.0, 7.348452, 1.837113]}, "(-0.25, +0.25)": {"two single-charge vector levels (low, high), m₃/₂²": [10.391921, 17.916312, 7.077058]}, "(+0.00, -0.25)": {"two single-charge vector levels (low, high), m₃/₂²": [3.086161, 4.262291, 1.837113]}, "(+0.00, +0.00)": {"two single-charge vector levels (low, high), m₃/₂²": [0.0, 2.0, 0.5]}, "(+0.00, +0.25)": {"two single-charge vector levels (low, high), m₃/₂²": [3.086161, 4.262291, 1.837113]}, "(+0.25, -0.25)": {"two single-charge vector levels (low, high), m₃/₂²": [10.391921, 17.916312, 7.077058]}, "(+0.25, +0.00)": {"two single-charge vector levels (low, high), m₃/₂²": [0.0, 7.348452, 1.837113]}, "(+0.25, +0.25)": {"two single-charge vector levels (low, high), m₃/₂²": [2.762196, 4.762196, 1.881098]}}, "max deviation (sum rule, tan²θ)": "<1e-09"}
  Q2_asymptotic_angles     {"α = 20°": {"tan²θ": "6.423e-06", "θ/π": 0.000807}, "α = 45°": {"tan²θ": "1.000e+00", "θ/π": 0.25}, "α = 70°": {"tan²θ": "1.550e+05", "θ/π": 0.499192}, "α = 135°": {"tan²θ": "1.000e+00", "θ/π": 0.25}}
  Q3_golden_boost          {"‖G − exp(ln φ · Y)‖": "<1e-12", "Y − Yᵀ": "<1e-12", "Y in e7 (relative residual)": "<1e-12", "[Y, D56], [Y, D_sol]": ["<1e-12", 0.529693], "projection of Y on span{D56, D_sol} (relative norm)": 0.385239, "spectrum of Y on the 56": [-1.0, -0.5, 0.0, 0.5, 1.0]}
  Q4_golden_line           {"t = 0.3": {"V": "<1e-12", "|∇V|": "<1e-12", "m₃/₂²": 0.546366, "gravitino spread": "<1e-09", "negative modes": 2, "lowest m²": -0.181354}, "t = 0.7": {"V": "<1e-12", "|∇V|": "<1e-12", "m₃/₂²": 0.787725, "gravitino spread": "<1e-09", "negative modes": 2, "lowest m²": -1.020676}, "t = 1.0": {"V": "<1e-12", "|∇V|": "<1e-12", "m₃/₂²": 1.190549, "gravitino spread": "<1e-09", "negative modes": 2, "lowest m²": -2.172323}, "t = 1.3": {"V": "<1e-12", "|∇V|": "<1e-12", "m₃/₂²": 1.942251, "gravitino spread": "<1e-09", "negative modes": 2, "lowest m²": -3.883657}, "rung 0": {"V": "<1e-12", "|∇V|": "<1e-12", "m₃/₂²": 0.5, "gravitino spread": "<1e-09", "negative modes": 0, "lowest m²": 0.0}, "rung 1": {"V": "<1e-12", "|∇V|": "<1e-12", "m₃/₂²": 0.625, "gravitino spread": "<1e-09", "negative modes": 2, "lowest m²": -0.472136}, "rung 2": {"V": "<1e-12", "|∇V|": "<1e-12", "m₃/₂²": 1.125, "gravitino spread": "<1e-09", "negative modes": 2, "lowest m²": -2.0}, "rung 3": {"V": "<1e-12", "|∇V|": "<1e-12", "m₃/₂²": 2.5, "gravitino spread": "<1e-09", "negative modes": 2, "lowest m²": -4.944272}, "rung ratios m₃/₂(n)/m₃/₂(0) vs (φⁿ + φ⁻ⁿ)/2": [[1.0, 1.0], [1.118034, 1.118034], [1.5, 1.5], [2.236068, 2.236068]]}
  receipt   PASS filed_d1414_house_frames_npz
  receipt   PASS s1275_results_fix_the_A1_normalisation
  computed  PASS Q1_on_the_torus_mu_A2_plus_mu_B2_equals_4_m32_squared_and_tan2_theta_equals_sinh2_4b_over_cosh2_4a
  computed  PASS Q2_theta_goes_to_0_in_the_a_sectors_to_pi2_in_the_b_sectors_and_to_pi4_on_both_diagonal_rays
  computed  PASS Q3_the_golden_boost_is_exp_lnphi_Y_with_Y_noncompact_in_e7_commuting_with_D56_not_D_sol
  computed  PASS Q4_the_golden_line_is_minkowski_and_stationary_with_m32_squared_half_cosh2_t_two_tachyons_minus4_cosh_t_minus_1_and_the_lucas_ladder_at_the_rungs
  argument  ARG  reading
  argument  ARG  scope
VERDICT: μ_A² + μ_B² = 4m₃/₂² on the torus — one KK angle, tan θ = sinh(4b)/cosh(4a), with single-tower channels in the sectors and dual ones on the diagonals; the golden boost is exp(ln φ Y) and its flow is a second Minkowski line through o with m₃/₂² = ½cosh²t, two tachyons −4(cosh t − 1), and the Lucas ladder m₃/₂(n)/m₃/₂(0) = (φⁿ + φ⁻ⁿ)/2 at the rungs. Tree level.
RESULT_HASH 689297e32d045f69
s1279: 4 computed, 2 receipt, 2 argument, 0 failed
