Check of 06-own-mark v2: N_f=1, t_f=1.00, m=3.00, clock spacing=0.50, levels k=[0, 1, 2]
Closed forms (6.6) vs general (6.5) at P=0, max abs difference of gamma^2 coefficients:
  6.66e-16

A. Dressed level E(0) and curvature E''(0): deviation exact - second order, slope in gamma
   coupling L  tau   k sigma | dE(g=0.01)  dE(g=0.08)  slope | dE''(g=0.01) dE''(g=0.08) slope | min gap
   (a)      6 1.00  0  +1   |   6.17e-07    3.04e-04  2.98 |   4.28e-07    2.07e-04  2.97 | 1.085
   (a)      6 1.00  0  -1   |  -9.10e-07   -4.81e-04  3.02 |   6.72e-07    3.48e-04  3.01 | 0.845
   (a)      6 1.00  1  +1   |   1.02e-06    4.99e-04  2.98 |   6.04e-07    2.89e-04  2.97 | 1.063
   (a)      6 1.00  1  -1   |  -1.42e-06   -7.54e-04  3.02 |   8.93e-07    4.64e-04  3.01 | 0.857
   (a)      6 1.00  2  +1   |   1.56e-06    7.59e-04  2.97 |   8.11e-07    3.84e-04  2.96 | 1.045
   (a)      6 1.00  2  -1   |  -2.09e-06   -1.11e-03  3.02 |   1.15e-06    5.96e-04  3.01 | 0.865
   (a)      6 0.25  0  +1   |   7.62e-07    3.74e-04  2.98 |   3.43e-08    1.64e-05  2.97 | 0.972
   (a)      6 0.25  0  -1   |  -7.89e-07   -4.18e-04  3.02 |   3.37e-08    1.75e-05  3.01 | 0.957
   (a)      6 0.25  1  +1   |   1.21e-06    5.91e-04  2.98 |   4.67e-08    2.21e-05  2.96 | 0.966
   (a)      6 0.25  1  -1   |  -1.25e-06   -6.67e-04  3.02 |   4.61e-08    2.41e-05  3.01 | 0.953
   (a)      6 0.25  2  +1   |   1.81e-06    8.76e-04  2.97 |   6.09e-08    2.86e-05  2.96 | 0.960
   (a)      6 0.25  2  -1   |  -1.87e-06   -1.00e-03  3.02 |   6.05e-08    3.16e-05  3.01 | 0.949
   (a)     10 1.00  0  +1   |   1.09e-06    5.17e-04  2.96 |   1.09e-06    5.02e-04  2.95 | 0.418
   (a)     10 1.00  0  -1   |  -1.80e-06   -9.97e-04  3.04 |   1.49e-06    8.65e-04  3.06 | 0.307
   (a)     10 1.00  1  +1   |   1.81e-06    8.40e-04  2.95 |   1.52e-06    6.85e-04  2.94 | 0.408
   (a)     10 1.00  1  -1   |  -2.78e-06   -1.56e-03  3.04 |   2.01e-06    1.17e-03  3.06 | 0.314
   (a)     10 1.00  2  +1   |   2.77e-06    1.27e-03  2.95 |   2.02e-06    8.90e-04  2.93 | 0.399
   (a)     10 1.00  2  -1   |  -4.06e-06   -2.30e-03  3.05 |   2.61e-06    1.53e-03  3.07 | 0.319
   (a)     10 0.25  0  +1   |   1.38e-06    6.48e-04  2.96 |   7.22e-08    3.23e-05  2.94 | 0.366
   (a)     10 0.25  0  -1   |  -1.46e-06   -8.11e-04  3.04 |   8.96e-08    4.96e-05  3.04 | 0.359
   (a)     10 0.25  1  +1   |   2.20e-06    1.01e-03  2.95 |   9.96e-08    4.35e-05  2.93 | 0.362
   (a)     10 0.25  1  -1   |  -2.32e-06   -1.30e-03  3.04 |   1.21e-07    6.76e-05  3.04 | 0.358
   (a)     10 0.25  2  +1   |   3.28e-06    1.49e-03  2.94 |   1.31e-07    5.61e-05  2.91 | 0.360
   (a)     10 0.25  2  -1   |  -3.47e-06   -1.97e-03  3.05 |   1.57e-07    8.85e-05  3.05 | 0.357
   (c)      6 1.00  0  +1   |   6.86e-07    3.37e-04  2.98 |   4.29e-07    2.11e-04  2.98 | 1.088
   (c)      6 1.00  0  -1   |  -9.85e-07   -5.23e-04  3.02 |   7.67e-07    4.14e-04  3.03 | 0.842
   (c)      6 1.00  1  +1   |   1.10e-06    5.36e-04  2.98 |   6.01e-07    2.92e-04  2.98 | 1.066
   (c)      6 1.00  1  -1   |  -1.51e-06   -8.02e-04  3.02 |   9.95e-07    5.38e-04  3.03 | 0.854
   (c)      6 1.00  2  +1   |   1.65e-06    8.00e-04  2.97 |   8.02e-07    3.86e-04  2.97 | 1.048
   (c)      6 1.00  2  -1   |  -2.19e-06   -1.17e-03  3.02 |   1.25e-06    6.78e-04  3.03 | 0.863
   (c)      6 0.25  0  +1   |   7.67e-07    3.77e-04  2.98 |   3.27e-08    1.61e-05  2.98 | 0.972
   (c)      6 0.25  0  -1   |  -7.93e-07   -4.20e-04  3.02 |   3.65e-08    1.96e-05  3.02 | 0.957
   (c)      6 0.25  1  +1   |   1.22e-06    5.93e-04  2.98 |   4.47e-08    2.17e-05  2.98 | 0.966
   (c)      6 0.25  1  -1   |  -1.26e-06   -6.69e-04  3.02 |   4.94e-08    2.66e-05  3.02 | 0.953
   (c)      6 0.25  2  +1   |   1.82e-06    8.79e-04  2.97 |   5.86e-08    2.82e-05  2.97 | 0.960
   (c)      6 0.25  2  -1   |  -1.88e-06   -1.00e-03  3.02 |   6.42e-08    3.47e-05  3.03 | 0.949
   (c)     10 1.00  0  +1   |   1.18e-06    5.53e-04  2.96 |   1.26e-06    5.87e-04  2.95 | 0.419
   (c)     10 1.00  0  -1   |  -1.91e-06   -1.06e-03  3.04 |   1.10e-06    7.05e-04  3.11 | 0.307
   (c)     10 1.00  1  +1   |   1.90e-06    8.80e-04  2.95 |   1.73e-06    7.87e-04  2.94 | 0.408
   (c)     10 1.00  1  -1   |  -2.90e-06   -1.63e-03  3.05 |   1.60e-06    1.01e-03  3.10 | 0.313
   (c)     10 1.00  2  +1   |   2.88e-06    1.31e-03  2.94 |   2.26e-06    1.01e-03  2.93 | 0.400
   (c)     10 1.00  2  -1   |  -4.20e-06   -2.38e-03  3.05 |   2.17e-06    1.37e-03  3.10 | 0.318
   (c)     10 0.25  0  +1   |   1.39e-06    6.50e-04  2.96 |   8.72e-08    3.99e-05  2.95 | 0.366
   (c)     10 0.25  0  -1   |  -1.47e-06   -8.14e-04  3.04 |   7.61e-08    4.36e-05  3.05 | 0.359
   (c)     10 0.25  1  +1   |   2.21e-06    1.02e-03  2.95 |   1.17e-07    5.24e-05  2.94 | 0.362
   (c)     10 0.25  1  -1   |  -2.33e-06   -1.31e-03  3.04 |   1.05e-07    6.09e-05  3.06 | 0.358
   (c)     10 0.25  2  +1   |   3.29e-06    1.49e-03  2.94 |   1.51e-07    6.62e-05  2.93 | 0.360
   (c)     10 0.25  2  -1   |  -3.48e-06   -1.97e-03  3.05 |   1.39e-07    8.11e-05  3.06 | 0.357

B. Clock spacings E_{k+1,+}(0)-E_{k,+}(0): exact - [(1+gamma n) spacing + gamma^2 (c2_{k+1}-c2_k)],
   slope in gamma; and the second-order change per unit spacing, (c2_{k+1}-c2_k)/spacing, for k=0,1
   (a) L= 6 tau=1.00 | k=0: dev(g=0.08)=1.95e-04 slope 2.97 | k=1: dev(g=0.08)=2.60e-04 slope 2.97 | change/spacing: k=0 -0.50477, k=1 -0.58530
   (a) L= 6 tau=0.25 | k=0: dev(g=0.08)=2.17e-04 slope 2.97 | k=1: dev(g=0.08)=2.85e-04 slope 2.97 | change/spacing: k=0 -0.52532, k=1 -0.60628
   (a) L=10 tau=1.00 | k=0: dev(g=0.08)=3.23e-04 slope 2.94 | k=1: dev(g=0.08)=4.28e-04 slope 2.93 | change/spacing: k=0 -0.50722, k=1 -0.58937
   (a) L=10 tau=0.25 | k=0: dev(g=0.08)=3.66e-04 slope 2.94 | k=1: dev(g=0.08)=4.76e-04 slope 2.93 | change/spacing: k=0 -0.53446, k=1 -0.61693
   (c) L= 6 tau=1.00 | k=0: dev(g=0.08)=1.99e-04 slope 2.97 | k=1: dev(g=0.08)=2.65e-04 slope 2.97 | change/spacing: k=0 -0.50378, k=1 -0.58472
   (c) L= 6 tau=0.25 | k=0: dev(g=0.08)=2.17e-04 slope 2.97 | k=1: dev(g=0.08)=2.85e-04 slope 2.97 | change/spacing: k=0 -0.52517, k=1 -0.60619
   (c) L=10 tau=1.00 | k=0: dev(g=0.08)=3.27e-04 slope 2.94 | k=1: dev(g=0.08)=4.32e-04 slope 2.93 | change/spacing: k=0 -0.50672, k=1 -0.58910
   (c) L=10 tau=0.25 | k=0: dev(g=0.08)=3.66e-04 slope 2.94 | k=1: dev(g=0.08)=4.76e-04 slope 2.93 | change/spacing: k=0 -0.53438, k=1 -0.61688

C. Leading-tau^2 curvature (6.11) vs full second-order curvature (6.10), relative deviation
   (a) L= 6 sigma=+1 k=0 | tau=0.2: 5.03e-03  tau=0.1: 1.25e-03  tau=0.05: 3.13e-04
   (a) L= 6 sigma=-1 k=0 | tau=0.2: 6.34e-03  tau=0.1: 1.59e-03  tau=0.05: 3.97e-04
   (a) L=10 sigma=+1 k=0 | tau=0.2: 1.57e-02  tau=0.1: 4.06e-03  tau=0.05: 1.02e-03
   (a) L=10 sigma=-1 k=0 | tau=0.2: 2.49e-03  tau=0.1: 5.95e-04  tau=0.05: 1.47e-04
   (c) L= 6 sigma=+1 k=0 | tau=0.2: 6.68e-03  tau=0.1: 1.67e-03  tau=0.05: 4.17e-04
   (c) L= 6 sigma=-1 k=0 | tau=0.2: 5.62e-03  tau=0.1: 1.41e-03  tau=0.05: 3.53e-04
   (c) L=10 sigma=+1 k=0 | tau=0.2: 3.80e-03  tau=0.1: 9.87e-04  tau=0.05: 2.49e-04
   (c) L=10 sigma=-1 k=0 | tau=0.2: 1.25e-02  tau=0.1: 3.03e-03  tau=0.05: 7.52e-04

D. Own mark (6.12): gamma^2 coefficients at P=0, sigma=+: cost c2E, curvature c2C,
   inertia change -(M^2/tau^4) c2C vs cost change / tau^2 = c2E/tau^2
   (a) L= 6 tau=1.00 k=0 M=3.00 | c2E=-0.65113 c2C=-0.207406 | inertia +1.8667  cost/tau^2 -0.6511
   (a) L= 6 tau=1.00 k=1 M=3.50 | c2E=-0.90352 c2C=-0.252117 | inertia +3.0884  cost/tau^2 -0.9035
   (a) L= 6 tau=1.00 k=2 M=4.00 | c2E=-1.19617 c2C=-0.297263 | inertia +4.7562  cost/tau^2 -1.1962
   (a) L= 6 tau=0.25 k=0 M=3.00 | c2E=-0.72366 c2C=-0.014699 | inertia +33.8660  cost/tau^2 -11.5785
   (a) L= 6 tau=0.25 k=1 M=3.50 | c2E=-0.98632 c2C=-0.017598 | inertia +55.1858  cost/tau^2 -15.7811
   (a) L= 6 tau=0.25 k=2 M=4.00 | c2E=-1.28946 c2C=-0.020503 | inertia +83.9800  cost/tau^2 -20.6314
   (a) L=10 tau=1.00 k=0 M=3.00 | c2E=-0.65269 c2C=-0.334776 | inertia +3.0130  cost/tau^2 -0.6527
   (a) L=10 tau=1.00 k=1 M=3.50 | c2E=-0.90630 c2C=-0.395481 | inertia +4.8446  cost/tau^2 -0.9063
   (a) L=10 tau=1.00 k=2 M=4.00 | c2E=-1.20099 c2C=-0.456167 | inertia +7.2987  cost/tau^2 -1.2010
   (a) L=10 tau=0.25 k=0 M=3.00 | c2E=-0.73610 c2C=-0.017649 | inertia +40.6627  cost/tau^2 -11.7776
   (a) L=10 tau=0.25 k=1 M=3.50 | c2E=-1.00333 c2C=-0.021398 | inertia +67.1055  cost/tau^2 -16.0533
   (a) L=10 tau=0.25 k=2 M=4.00 | c2E=-1.31180 c2C=-0.025154 | inertia +103.0315  cost/tau^2 -20.9888
   (c) L= 6 tau=1.00 k=0 M=3.00 | c2E=-0.68067 c2C=-0.268163 | inertia +2.4135  cost/tau^2 -0.6807
   (c) L= 6 tau=1.00 k=1 M=3.50 | c2E=-0.93256 c2C=-0.314727 | inertia +3.8554  cost/tau^2 -0.9326
   (c) L= 6 tau=1.00 k=2 M=4.00 | c2E=-1.22492 c2C=-0.361271 | inertia +5.7803  cost/tau^2 -1.2249
   (c) L= 6 tau=0.25 k=0 M=3.00 | c2E=-0.72573 c2C=-0.019472 | inertia +44.8645  cost/tau^2 -11.6116
   (c) L= 6 tau=0.25 k=1 M=3.50 | c2E=-0.98831 c2C=-0.022371 | inertia +70.1550  cost/tau^2 -15.8130
   (c) L= 6 tau=0.25 k=2 M=4.00 | c2E=-1.29141 c2C=-0.025268 | inertia +103.4980  cost/tau^2 -20.6625
   (c) L=10 tau=1.00 k=0 M=3.00 | c2E=-0.67330 c2C=-0.447612 | inertia +4.0285  cost/tau^2 -0.6733
   (c) L=10 tau=1.00 k=1 M=3.50 | c2E=-0.92666 c2C=-0.513972 | inertia +6.2962  cost/tau^2 -0.9267
   (c) L=10 tau=1.00 k=2 M=4.00 | c2E=-1.22121 c2C=-0.579069 | inertia +9.2651  cost/tau^2 -1.2212
   (c) L=10 tau=0.25 k=0 M=3.00 | c2E=-0.73755 c2C=-0.027660 | inertia +63.7277  cost/tau^2 -11.8008
   (c) L=10 tau=0.25 k=1 M=3.50 | c2E=-1.00474 c2C=-0.031422 | inertia +98.5408  cost/tau^2 -16.0758
   (c) L=10 tau=0.25 k=2 M=4.00 | c2E=-1.31317 c2C=-0.035182 | inertia +144.1058  cost/tau^2 -21.0108