Verification run 2 -- G: remarks of Section 7 and the numbers of Figure 1
PASS  Remark 7.1: tau(p) <= tau(0) max mu_p / min mu_p   (40 graphs, 10 values of p; largest left/right = 0.9995)
PASS  Remark 7.1: on these graphs max mu_p / min mu_p increases along the grid and is large near p = 1 (the bound is not decreasing)
   C_12: tau(0) = 7.464102; turning points on the grid k/400: [('max', 0.0825, 8.84961)]; tau(0.9999) = 2.02470
PASS  Figure 1(a): C_12: tau(0) = 7.46, one turning point, a maximum 8.85 near p = 0.08; d = 2
   Z/16 {+-3,+-5,8}: d = 5; tau(0) = 4.267767; turning points: [('max', 0.2275, 5.68346), ('min', 0.8125, 4.81074)]; tau(0.9999) = 4.99982
PASS  Figure 1(c): Z/16, S = {+-3,+-5,8}: tau(0) = 4.27, local maximum 5.68 near 0.23, local minimum 4.81 near 0.81, then increasing to d = 5
PASS     the same with exact targets and 30 digits: tau(0.2275) = 5.6834629 is above tau(0.22), tau(0.235); tau(0.8125) = 4.8107448 is below tau(0.79), tau(0.835)
   Z/21 {+-2,+-7,+-9}: d = 6; tau(0) = 3.983956; turning points: [('max', 0.41, 5.92294), ('min', 0.725, 5.85421)]; tau(0.9999) = 5.99989
PASS  Remark 7.3: Z/21, S = {+-2,+-7,+-9}: local maximum 5.923 near p = 0.41, local minimum 5.854 near p = 0.725, d = 6
   C_5: max_p tau(p)/tau(0) = 1.6928 at p = 7.316e-01 (p n^2 = 18.29); up-then-down on a grid of 240 values: True
   C_6: max_p tau(p)/tau(0) = 1.4735 at p = 4.850e-01 (p n^2 = 17.46); up-then-down on a grid of 240 values: True
   C_7: max_p tau(p)/tau(0) = 1.3754 at p = 3.455e-01 (p n^2 = 16.93); up-then-down on a grid of 240 values: True
   C_8: max_p tau(p)/tau(0) = 1.3058 at p = 2.422e-01 (p n^2 = 15.50); up-then-down on a grid of 240 values: True
   C_10: max_p tau(p)/tau(0) = 1.2286 at p = 1.337e-01 (p n^2 = 13.37); up-then-down on a grid of 240 values: True
   C_12: max_p tau(p)/tau(0) = 1.1856 at p = 8.199e-02 (p n^2 = 11.81); up-then-down on a grid of 240 values: True
   C_16: max_p tau(p)/tau(0) = 1.1403 at p = 3.849e-02 (p n^2 = 9.85); up-then-down on a grid of 240 values: True
   C_20: max_p tau(p)/tau(0) = 1.1170 at p = 2.182e-02 (p n^2 = 8.73); up-then-down on a grid of 240 values: True
   C_24: max_p tau(p)/tau(0) = 1.1030 at p = 1.391e-02 (p n^2 = 8.01); up-then-down on a grid of 240 values: True
   C_32: max_p tau(p)/tau(0) = 1.0870 at p = 6.987e-03 (p n^2 = 7.16); up-then-down on a grid of 240 values: True
   C_48: max_p tau(p)/tau(0) = 1.0728 at p = 2.755e-03 (p n^2 = 6.35); up-then-down on a grid of 240 values: True
   C_64: max_p tau(p)/tau(0) = 1.0662 at p = 1.455e-03 (p n^2 = 5.96); up-then-down on a grid of 240 values: True
   C_96: max_p tau(p)/tau(0) = 1.0600 at p = 6.064e-04 (p n^2 = 5.59); up-then-down on a grid of 240 values: True
   C_128: max_p tau(p)/tau(0) = 1.0571 at p = 3.300e-04 (p n^2 = 5.41); up-then-down on a grid of 240 values: True
   C_192: max_p tau(p)/tau(0) = 1.0542 at p = 1.418e-04 (p n^2 = 5.23); up-then-down on a grid of 240 values: True
   C_256: max_p tau(p)/tau(0) = 1.0528 at p = 7.843e-05 (p n^2 = 5.14); up-then-down on a grid of 240 values: True
PASS  Remark 7.3: on C_n (16 values of n from 5 to 256) tau goes up and then down, and max tau/tau(0) decreases from 1.69 (n = 5) to 1.05 (n = 256)

checks passed: 7   TOTAL failures: 0
