s1281 — the KK angle off o, in three lenses
  Q1_spin_half_on_the_torus      {"at o: raw A3 singular values / min; goldstino rank; normalisation c·(raw scale)": [{"1.0": 40, "2.0": 8, "3.0": 8}, 8, 1.0], "grid": {"(-0.25, -0.25)": {"goldstino rank": 8, "spin-½ m² levels": {"1.881098": 32, "7.405489": 8, "11.405489": 8}}, "(-0.25, +0.00)": {"goldstino rank": 8, "spin-½ m² levels": {"1.837113": 40, "16.534017": 8}}, "(-0.25, +0.25)": {"goldstino rank": 8, "spin-½ m² levels": {"7.077058": 32, "27.8609": 8, "42.909682": 8}}, "(+0.00, -0.25)": {"goldstino rank": 8, "spin-½ m² levels": {"1.837113": 32, "8.009436": 8, "10.361694": 8}}, "(+0.00, +0.00)": {"goldstino rank": 8, "spin-½ m² levels": {"0.5": 40, "4.5": 8}}, "(+0.00, +0.25)": {"goldstino rank": 8, "spin-½ m² levels": {"1.837113": 32, "8.009436": 8, "10.361694": 8}}, "(+0.25, -0.25)": {"goldstino rank": 8, "spin-½ m² levels": {"7.077058": 32, "27.8609": 8, "42.909682": 8}}, "(+0.25, +0.00)": {"goldstino rank": 8, "spin-½ m² levels": {"1.837113": 40, "16.534017": 8}}, "(+0.25, +0.25)": {"goldstino rank": 8, "spin-½ m² levels": {"1.881098": 32, "7.405489": 8, "11.405489": 8}}, "(+0.10, -0.20)": {"goldstino rank": 8, "spin-½ m² levels": {"1.772134": 32, "7.484623": 8, "10.236713": 8}}}, "max relative deviation from √(μ_A²n₁² + μ_B²n₂²), |n| = (½,½)×32, (½,3/2)×8, (3/2,½)×8": "<1e-09", "controls (max relative deviation): sesquilinear projection; conjugate goldstino space": [0.634102, 0.652948]}
  Q2_moments_and_supertraces     {"dof (bosonic, fermionic), eaten-corrected": [128, 128], "signed moments Σ±dof·n₁₂^{2i}n₇₈^{2j}": {"(0, 0)": "0", "(0, 1)": "0", "(1, 0)": "0", "(0, 2)": "0", "(1, 1)": "0", "(2, 0)": "0", "(0, 3)": "0", "(1, 2)": "0", "(2, 1)": "0", "(3, 0)": "0", "(0, 4)": "315/2", "(1, 3)": "-45/2", "(2, 2)": "27/2", "(3, 1)": "-45/2", "(4, 0)": "315/2"}, "STr M^{2k}, k = 0…4, as polynomials in (A = μ_A², B = μ_B²)": ["0", "0", "0", "0", "315*A**4/2 - 90*A**3*B + 81*A**2*B**2 - 90*A*B**3 + 315*B**4/2"], "numeric STr M^{2k} (k = 0…3 relative; k = 4 absolute) with the computed spin-½": {"(+0.25, +0.25)": ["<1e-09", "<1e-09", "<1e-09", "<1e-09", 68307.53967], "(-0.25, +0.25)": ["<1e-09", "<1e-09", "<1e-09", "<1e-09", 13684664.980659], "(+0.10, -0.20)": ["<1e-09", "<1e-09", "<1e-09", "<1e-09", 44489.252628]}}
  Q3_one_loop_shape_potential    {"g(0), g(π/8), g(π/4), g(3π/8)": [-185.92, -107.21862, -45.430582, -107.21862], "g increasing on (0, π/4]": true, "μ-independence |V₁(μ² = 1) − V₁(μ² = 7)| at (0.1, −0.2)": "<1e-09", "V₁ = m₃/₂⁴ g(θ) at (0.1, −0.2) (relative)": "<1e-09", "64π²V₁(o); |∇| at o; Hessian eigenvalues at o (rounded)": [-46.47947, "<1e-06", [-4790, 2294]]}
  Q4_charge_torus_and_the_braid  {"tr₅₆ Gram of (Q₁₂, Q₇₈)": [[-24.0, 0.0], [0.0, -24.0]], "Q₇₈ − Z": "<1e-12", "relative residual of gQ₁₂g⁻¹, gQ₇₈g⁻¹ outside span{Q₁₂, Q₇₈}": {"B1": ["<1e-12", 1.0], "B2": ["<1e-12", 1.0], "W_h": ["<1e-12", 0.5], "G": ["<1e-12", 1.0], "O": ["<1e-12", "<1e-12"]}, "B1, B2, W_h commute with Q₁₂": "<1e-12", "W_h spectral radius on the 56": 2.618034, "modular: P·W_F1·P⁻¹ − [[2,1],[1,1]]; S W S⁻¹ − W⁻¹; fixed points; axis ∩ imaginary axis; translation length / ln φ": ["True", "True", ["1/2 + sqrt(5)/2", "1/2 - sqrt(5)/2"], "[-1, 1]", 4.0]}
  Q5_number_theory               {"coincident |charge| pairs in 2|n| ≤ 6: θ = π/4, tan²θ = 1/2, tan²θ = φ⁻², tan θ = sinh 1": [25, 6, 0, 0], "a = b = n ln φ / 4: |1 − tan²θ − (4/(5F_n²) odd, 4/L_n² even)|, n = 1…6": ["<1e-12", "<1e-12", "<1e-12", "<1e-12", "<1e-12", "<1e-12"]}
  receipt   PASS filed_d1414_house_frames_npz
  receipt   PASS filed_chatgpt_d1414_maps_npz
  receipt   PASS s1276_results_charge_tables_and_the_t2_formula
  receipt   PASS s1275_results_su8_frame_A1_A2_machinery
  receipt   PASS s1274_results_torus_closed_forms
  computed  PASS Q1_the_48_physical_spin_half_masses_obey_the_t2_formula_on_the_whole_torus_with_one_constant_fixed_at_o_and_both_controls_fail
  computed  PASS Q2_boson_and_fermion_charge_moments_agree_to_degree_six_so_STr_M0_M2_M4_M6_vanish_on_the_whole_torus_and_STr_M8_does_not
  computed  PASS Q3_the_one_loop_potential_is_scale_free_m32_4_g_theta_g_peaks_at_the_diagonal_and_o_is_a_saddle
  computed  PASS Q4_the_charge_torus_has_a_square_e7_trace_form_the_braid_fixes_Q12_and_moves_Z_off_the_torus_and_the_figure8_axis_meets_tau_i
  computed  PASS Q5_accidental_mass_coincidences_need_rational_tan2_theta_golden_and_generic_angles_have_none_and_the_golden_rungs_are_pell_arithmetic
  argument  ARG  category_lens
  argument  ARG  knot_lens
  argument  ARG  number_lens
  argument  ARG  scope
VERDICT: the whole radius-torus spectrum, spin-½ included, is m² = 4m₃/₂²(n₁₂² sin²θ + n₇₈² cos²θ) — one KK angle; boson and fermion charge moments agree to degree six, so STr M^{0,2,4,6} = 0 everywhere; the one-loop shape potential m₃/₂⁴ g(θ) peaks at the diagonal (o a saddle); the charge torus carries a square definite E7 form, so no E7 symmetry acts on it hyperbolically and the figure-8 braid cannot move the KK shape. Tree level; V₁ probe-grade.
RESULT_HASH 0ef83cb72cb25fcc
s1281: 5 computed, 5 receipt, 4 argument, 0 failed
