certificate A: gamma=0.666667 kappa=2.5819888975  max ratio found=2.4554706524  at [0.099044, 0.441306, 0.484115, 0.549274, 0.626238, 0.888631]
   n=1 ratios at t=0,0.25,0.5,0.75,1: [1.632993, 1.838181, 1.897991, 1.838181, 1.632993]
certificate B: gamma=0.500000 kappa=2.4494897428  max ratio found=2.3525612167  at [0.315101, 0.551186, 0.570065, 0.588303, 0.597025, 0.719577]
   n=1 ratios at t=0,0.25,0.5,0.75,1: [1.535932, 2.035401, 2.251354, 2.035401, 1.535932]
identity (iii) of Lemma A: largest |lhs - rhs| over 600 random tests = 1.776e-15
