HD k=1: 9 >= 9: True
HD k=2: 27/2 >= 12: True
HD k=3: 9/4 >= 9/4: True
family A_n = (J-I)/(n-1): first partial-sum index k where sum_{i<=k} lambda_i(P) > sum_{i<=k} lambda_i(P_inf)
  n=3: lambda_1(P)=1.8660254 <= lambda_1(Pinf)=2.0966484; violated k: [2]; max gap 0.00461692
  n=4: lambda_1(P)=2.2152504 <= lambda_1(Pinf)=2.3487677; violated k: []; max gap -0.00867948
  n=5: lambda_1(P)=2.4394274 <= lambda_1(Pinf)=2.5281602; violated k: []; max gap -0.00202492
  n=6: lambda_1(P)=2.6000264 <= lambda_1(Pinf)=2.6638123; violated k: []; max gap -0.00115221
  n=7: lambda_1(P)=2.7225187 <= lambda_1(Pinf)=2.7708183; violated k: []; max gap -0.000600916
  n=8: lambda_1(P)=2.819928 <= lambda_1(Pinf)=2.8578915; violated k: []; max gap -0.000353798
  n=9: lambda_1(P)=2.8997596 <= lambda_1(Pinf)=2.9304524; violated k: []; max gap -0.000220557
  n=10: lambda_1(P)=2.9666998 <= lambda_1(Pinf)=2.9920697; violated k: []; max gap -0.000144666
  n=11: lambda_1(P)=3.0238515 <= lambda_1(Pinf)=3.0451993; violated k: []; max gap -9.8784e-5
  n=12: lambda_1(P)=3.0733636 <= lambda_1(Pinf)=3.0915934; violated k: []; max gap -6.97374e-5
bivariate D_(2,3): 398 random members tested; max over k of (partial sum P - partial sum P_inf) = 0.0
exit 0
