s1310 — the Fibonacci vector of the figure-8 complement and its fillings
  V1_coloured_invariants     {"J_1": "1", "J_τ(z) − (1 − √5) ≡ 0 mod Φ₁₀": true, "[3]_z − φ ≡ 0 mod Φ₁₀": true, "CONTROL J_τ(z) − (1 + √5) ≡ 0 mod Φ₁₀ (must be False)": false, "√5 identity: s5(ζ) − √5 (numeric)": "<1e-14", "|q⁴ − T_F[τ, τ]|": "<1e-15", "J_τ (numeric)": -1.236067977, "|Im J_τ(ζ)|": "<1e-14"}
  V2_complement_vector       {"v = S_{0b} J_b (meridian basis)": [0.525731112, -1.051462224], "D·v": [1.0, -2.0], "S_F·v (longitude basis)": [-0.618033989, 1.0]}
  V3_fillings                {"unknot: Z(±1) − 1/D, Z(0) − 1": ["<1e-12", "<1e-12", "<1e-12"], "Z(S³_0(4₁)) and + φ⁻¹": [-0.618033989, "<1e-12"], "|Tr ρ(A)| (s1302 route) − |Z(S³_0(4₁))|": "<1e-12", "max_n |Z(−n) − conj Z(n)| (amphichirality)": "<1e-12", "|Z(S³_n(4₁))|, n = 0..6": [0.618033989, 1.129775731, 0.850650808, 0.850650808, 1.129775731, 0.618033989, 1.129775731], "period 5 in n ≥ 1: max_n |Z(n+5)| − |Z(n)| (n = 1..6); |Z(5)| − |Z(0)|": ["<1e-12", "<1e-12"]}
  V4_framing_anomaly         {"|Δ₊| − D": "<1e-12", "arg(Δ₊/D)/2π − (14/5)/8": "<1e-12", "Δ₋ − conj Δ₊": "<1e-12"}
  V5_V56_coefficients        {"tr W_h": 68.0, "|Tr(ρ(A) ⊗ W_h) − Tr ρ(A)·tr W_h|": "<1e-09"}
  receipt   PASS filed_d1414_house_frames_npz
  receipt   PASS s1302_results_torus_bundle_value_and_modular_data
  computed  PASS V1_exact_in_Q_zeta10_J_tau_of_the_figure8_is_1_minus_sqrt5_and_the_quantum_dimension_is_phi_with_the_wrong_sign_control_failing
  computed  PASS V2_the_complement_vector_is_1_minus2_over_D
  computed  PASS V3_unknot_controls_hold_the_zero_filling_is_minus_inverse_phi_equal_in_modulus_to_the_s1302_bundle_trace_and_amphichirality_conjugates
  symbolic  PASS V3_exact_zero_filling_value_is_minus_inverse_phi
  computed  PASS V4_the_framing_anomaly_is_e_2pi_i_c_over_8_with_c_14_over_5
  computed  PASS V5_the_naive_V56_coefficient_trace_is_the_product_so_it_carries_no_new_information
  argument  ARG  reading
  argument  ARG  scope
VERDICT: the figure-8 complement has Fibonacci vector (1, −2)/D; its 0-filling reproduces the s1302 torus-bundle value (−φ⁻¹, modulus φ⁻¹) by an independent route; ±n fillings are complex conjugate (amphichirality); the framing anomaly is e^{2πi c/8}, c = 14/5; a V56 trace factorises.
RESULT_HASH 2603dccad61c1664
s1310: 5 computed, 1 symbolic, 2 receipt, 2 argument, 0 failed
