s1302 — a TQFT on the mapping torus of the fibre monodromy
  K1_W_h                     {"max |W_h − round(W_h)|": "<1e-09", "charpoly == (t²−3t+1)¹²(t−1)³²": true, "tr W_hⁿ vs 12·L_2n + 32 (n=1..5)": [[68, 68], [116, 116], [248, 248], [596, 596], [1508, 1508]]}
  K2_torsion                 {"rows": [{"n": 2, "|det(Aⁿ−I)|": 5, "Fox ∏Δ(ζ_n^k)": 5, "L_2n − 2": 5}, {"n": 3, "|det(Aⁿ−I)|": 16, "Fox ∏Δ(ζ_n^k)": 16, "L_2n − 2": 16}, {"n": 4, "|det(Aⁿ−I)|": 45, "Fox ∏Δ(ζ_n^k)": 45, "L_2n − 2": 45}, {"n": 5, "|det(Aⁿ−I)|": 121, "Fox ∏Δ(ζ_n^k)": 121, "L_2n − 2": 121}, {"n": 6, "|det(Aⁿ−I)|": 320, "Fox ∏Δ(ζ_n^k)": 320, "L_2n − 2": 320}, {"n": 7, "|det(Aⁿ−I)|": 841, "Fox ∏Δ(ζ_n^k)": 841, "L_2n − 2": 841}, {"n": 8, "|det(Aⁿ−I)|": 2205, "Fox ∏Δ(ζ_n^k)": 2205, "L_2n − 2": 2205}], "Δ(−1)": 5, "disc Δ": 5}
  K3_modular_data            {"|S²−I|": "<1e-14", "|SS†−I|": "<1e-14", "|(ST)³ − e^{2πi c/8}I|, c = 14/5": "<1e-14", "|T⁵ − I|": "<1e-14"}
  K4_fibonacci_invariant     {"|Z(T_{Aⁿ})| n = 1..10": [0.61803398875, 1.61803398875, 1.61803398875, 0.61803398875, 2.0, 0.61803398875, 1.61803398875, 1.61803398875, 0.61803398875, 2.0], "max dev from (φ⁻¹, φ, φ, φ⁻¹, 2) periodic, n ≤ 20": "<1e-12", "projective order of ρ(A)": 5, "eigenvalue ratio / 2π (mod 1)": 0.4}
  K5_exact                   {"|Z(T_A)|²": "|1 − ζ₅|²/D² = (2 − 2cos(2π/5))/(2 + φ) = φ⁻² = (3 − √5)/2"}
  K6_mod_5                   {"A mod 5": [[3, 4], [1, 0]], "N = A + I mod 5": [[4, 4], [1, 1]], "N² mod 5": [[0, 0], [0, 0]], "A⁵ mod 5": [[4, 0], [0, 4]], "Δ mod 5 == (t+1)²": true}
  K7_two_fibonacci_objects   {"eigenvalue-ratio order, braid generator R (A1776 fibre; any scalar twist ν)": 10, "eigenvalue-ratio order, modular T_F on V(T²)": 5}
  K8_orientation_reversal    {"spec ρ(T) == spec ρ(T)⁻¹ (needed for a LINEAR extension)": false, "|conj ρ(T) − ρ(T)⁻¹|": "<1e-14", "|conj ρ(S) − ρ(S)|": "<1e-14", "|Z| at [[2,1],[1,1]] (the squared Gieseking class)": 0.61803398875}
  receipt   PASS filed_d1414_house_frames_npz
  receipt   PASS s706_results_fibonacci_checks_all_pass
  computed  PASS K1_the_charpoly_of_W_h_is_the_alexander_polynomial_to_the_twelfth_times_t_minus_1_to_the_32nd_and_tr_W_h_n_is_12_L2n_plus_32
  computed  PASS K2_the_torsion_of_the_torus_bundle_equals_the_fox_cyclic_cover_product_equals_L2n_minus_2_and_delta_minus_1_is_5
  computed  PASS K3_the_fibonacci_modular_data_satisfy_S2_I_unitarity_ST_cubed_central_charge_14_over_5_and_T_has_order_5
  computed  PASS K4_the_fibonacci_invariant_of_the_mapping_torus_has_modulus_inverse_phi_phi_phi_inverse_phi_2_with_period_5
  symbolic  PASS K5_the_modulus_squared_of_the_fibonacci_invariant_at_n_1_is_phi_to_minus_2
  computed  PASS K6_the_monodromy_is_minus_unipotent_mod_5_so_A5_is_minus_I_mod_5_and_rho_A5_is_scalar
  computed  PASS K7_the_fibonacci_braid_fibre_and_the_modular_representation_on_V_T2_are_projectively_inequivalent
  computed  PASS K8_no_linear_extension_to_the_orientation_reversing_class_complex_conjugation_extends_and_the_squared_class_has_modulus_inverse_phi
  argument  ARG  reading
  argument  ARG  what_is_still_unbuilt
VERDICT: the mapping torus of A = T³S carries torsion L_2n − 2 (Lucas, = Fox) and a Fibonacci invariant of modulus φ⁻¹, φ, φ, φ⁻¹, 2 with period 5, forced by A ≡ −unipotent mod 5 (5 = disc = Δ(−1)); the braid fibre and the modular representation are different Fibonacci objects; the Gieseking class has no oriented value.
RESULT_HASH 1f8a66fde68f719d
s1302: 7 computed, 1 symbolic, 2 receipt, 2 argument, 0 failed
