1. (5.13) at t_f = 0, N_f = 1, G = |gamma| M_k = 1: exact E''(0) of the lower level vs leading winding term
   L   tau/G   E'' exact        (5.13) leading   ratio    (1 - ratio)/(L tau^2/G^2)
   5   0.10   -9.478120e-12   -9.765625e-12   0.97056   0.589
   5   0.20   -8.885691e-09   -1.000000e-08   0.88857   0.557
   6   0.10   -1.102813e-06   -1.125000e-06   0.98028   0.329
   6   0.20   -6.655007e-05   -7.200000e-05   0.92431   0.315
   7   0.20   -1.674216e-12   -1.960000e-12   0.85419   0.521
   7   0.30   -4.040328e-10   -5.721814e-10   0.70613   0.466
   8   0.10   +4.877034e-09   +5.000000e-09   0.97541   0.307
   8   0.20   +1.160004e-06   +1.280000e-06   0.90625   0.293

2. Order of limits, L = 6, N_f = 1, G = 1, tau = 0.2 (d_{k,sigma_l} -> |g| = 1 as t_f -> 0):
   t_f      E'' exact       2 tau^2 J (order tau^2)   E''(t_f=0)
   0.300   -2.7046e-02     -3.0795e-02               -6.6550e-05
   0.100   -2.8229e-03     -3.2514e-03               -6.6550e-05
   0.050   -7.4565e-04     -8.0343e-04               -6.6550e-05
   0.020   -1.7473e-04     -1.2809e-04               -6.6550e-05
   0.010   -9.3578e-05     -3.2006e-05               -6.6550e-05
   0.005   -7.3306e-05     -8.0003e-06               -6.6550e-05
   0.002   -6.7631e-05     -1.2800e-06               -6.6550e-05
   0.001   -6.6820e-05     -3.2000e-07               -6.6550e-05
   0.000   -6.6550e-05     +0.0000e+00               -6.6550e-05
   2 tau^2 J / (tau^2 t_f^2) at t_f = 0.001: -8.0000 (J = O(t_f^{2 N_f}))