Verification run 2 -- H: all Cayley graphs of the groups of order <= 12
grid of 209 values of p: [0.0, 1e-06, 1e-05, 0.0001, 0.001, 0.005, 0.01, 0.015, 0.02, 0.025, 0.03, 0.035, 0.04, 0.045, 0.05, 0.055, 0.06, 0.065, 0.07, 0.075, 0.08, 0.085, 0.09, 0.095, 0.1, 0.105, 0.11, 0.115, 0.12, 0.125, 0.13, 0.135, 0.14, 0.145, 0.15, 0.155, 0.16, 0.165, 0.17, 0.175, 0.18, 0.185, 0.19, 0.195, 0.2, 0.205, 0.21, 0.215, 0.22, 0.225, 0.23, 0.235, 0.24, 0.245, 0.25, 0.255, 0.26, 0.265, 0.27, 0.275, 0.28, 0.285, 0.29, 0.295, 0.3, 0.305, 0.31, 0.315, 0.32, 0.325, 0.33, 0.335, 0.34, 0.345, 0.35, 0.355, 0.36, 0.365, 0.37, 0.375, 0.38, 0.385, 0.39, 0.395, 0.4, 0.405, 0.41, 0.415, 0.42, 0.425, 0.43, 0.435, 0.44, 0.445, 0.45, 0.455, 0.46, 0.465, 0.47, 0.475, 0.48, 0.485, 0.49, 0.495, 0.5, 0.505, 0.51, 0.515, 0.52, 0.525, 0.53, 0.535, 0.54, 0.545, 0.55, 0.555, 0.56, 0.565, 0.57, 0.575, 0.58, 0.585, 0.59, 0.595, 0.6, 0.605, 0.61, 0.615, 0.62, 0.625, 0.63, 0.635, 0.64, 0.645, 0.65, 0.655, 0.66, 0.665, 0.67, 0.675, 0.68, 0.685, 0.69, 0.695, 0.7, 0.705, 0.71, 0.715, 0.72, 0.725, 0.73, 0.735, 0.74, 0.745, 0.75, 0.755, 0.76, 0.765, 0.77, 0.775, 0.78, 0.785, 0.79, 0.795, 0.8, 0.805, 0.81, 0.815, 0.82, 0.825, 0.83, 0.835, 0.84, 0.845, 0.85, 0.855, 0.86, 0.865, 0.87, 0.875, 0.88, 0.885, 0.89, 0.895, 0.9, 0.905, 0.91, 0.915, 0.92, 0.925, 0.93, 0.935, 0.94, 0.945, 0.95, 0.955, 0.96, 0.965, 0.97, 0.975, 0.98, 0.985, 0.99, 0.995, 0.9975, 0.999, 0.9999, 0.99999, 0.999999]
second grid of 24 values of p, for a comparison of the shapes: [0.0, 0.01, 0.03, 0.06, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6, 0.65, 0.7, 0.75, 0.8, 0.85, 0.9, 0.95, 0.98, 0.995]
23 groups, pairwise non-isomorphic (distinguished by order, commutativity and the numbers of elements of each order)
groups by order: 2: Z_2; 3: Z_3; 4: Z_4, Z_2^2; 5: Z_5; 6: Z_6, S_3; 7: Z_7; 8: Z_8, Z_2 x Z_4, Z_2^3, D_4, Q_8; 9: Z_9, Z_3^2; 10: Z_10, D_5; 11: Z_11; 12: Z_12, Z_2 x Z_6, A_4, D_6, Dic_3
Z_2        order  2:    1 symmetric generating sets; shapes on the grid: {'increasing': 1}
Z_3        order  3:    1 symmetric generating sets; shapes on the grid: {'increasing': 1}
Z_4        order  4:    2 symmetric generating sets; shapes on the grid: {'increasing': 2}
Z_5        order  5:    3 symmetric generating sets; shapes on the grid: {'up-then-down': 2, 'increasing': 1}
Z_6        order  6:    5 symmetric generating sets; shapes on the grid: {'up-then-down': 1, 'increasing': 4}
Z_7        order  7:    7 symmetric generating sets; shapes on the grid: {'up-then-down': 3, 'increasing': 4}
Z_8        order  8:   12 symmetric generating sets; shapes on the grid: {'up-then-down': 4, 'increasing': 8}
Z_9        order  9:   14 symmetric generating sets; shapes on the grid: {'up-then-down': 6, 'increasing': 8}
Z_10       order 10:   27 symmetric generating sets; shapes on the grid: {'up-then-down': 11, 'increasing': 16}
Z_11       order 11:   31 symmetric generating sets; shapes on the grid: {'up-then-down': 15, 'increasing': 16}
Z_12       order 12:   54 symmetric generating sets; shapes on the grid: {'up-then-down': 18, 'increasing': 36}
Z_2^2      order  4:    4 symmetric generating sets; shapes on the grid: {'increasing': 4}
Z_2 x Z_4  order  8:   20 symmetric generating sets; shapes on the grid: {'up-then-down': 4, 'increasing': 16}
Z_2^3      order  8:   92 symmetric generating sets; shapes on the grid: {'up-then-down': 28, 'increasing': 64}
Z_3^2      order  9:   11 symmetric generating sets; shapes on the grid: {'increasing': 11}
Z_2 x Z_6  order 12:  104 symmetric generating sets; shapes on the grid: {'up-then-down': 36, 'increasing': 68}
S_3        order  6:   11 symmetric generating sets; shapes on the grid: {'increasing': 8, 'up-then-down': 3}
D_4        order  8:   48 symmetric generating sets; shapes on the grid: {'up-then-down': 16, 'increasing': 32}
Q_8        order  8:    8 symmetric generating sets; shapes on the grid: {'increasing': 8}
D_5        order 10:  119 symmetric generating sets; shapes on the grid: {'up-then-down': 55, 'increasing': 64}
A_4        order 12:  116 symmetric generating sets; shapes on the grid: {'up-then-down': 36, 'increasing': 80}
D_6        order 12:  464 symmetric generating sets; shapes on the grid: {'up-then-down': 190, 'increasing': 274}
Dic_3      order 12:   50 symmetric generating sets; shapes on the grid: {'up-then-down': 12, 'increasing': 38}

total number of Cayley graphs (symmetric generating sets without the identity): 1204
shapes on the grid: {'increasing': 764, 'up-then-down': 440}
violations of Lemma 2.1(b), Theorem 1.2, Theorem 1.3 or the sign in Theorem 1.6: 0
graphs whose shape on the second grid differs from the shape on the first grid: 12
   D_6 S = [1, 2, 3, 7, 10]: first grid up-then-down, second grid increasing
   D_6 S = [1, 2, 5, 7, 10]: first grid up-then-down, second grid increasing
   D_6 S = [1, 2, 3, 9, 10]: first grid up-then-down, second grid increasing
   D_6 S = [2, 3, 5, 9, 10]: first grid up-then-down, second grid increasing
   D_6 S = [1, 2, 7, 9, 10]: first grid up-then-down, second grid increasing
   D_6 S = [2, 3, 7, 9, 10]: first grid up-then-down, second grid increasing
   D_6 S = [1, 2, 5, 10, 11]: first grid up-then-down, second grid increasing
   D_6 S = [2, 3, 5, 10, 11]: first grid up-then-down, second grid increasing
   D_6 S = [1, 2, 7, 10, 11]: first grid up-then-down, second grid increasing
   D_6 S = [2, 5, 7, 10, 11]: first grid up-then-down, second grid increasing
   D_6 S = [2, 3, 9, 10, 11]: first grid up-then-down, second grid increasing
   D_6 S = [2, 5, 9, 10, 11]: first grid up-then-down, second grid increasing
PASS  the number of Cayley graphs of the 23 groups of order <= 12 is 1204
PASS  no violation of any tested statement
