(1) D_1(Pi, B_N) for d = 2, exact
  N= 1  D1=1/3  (1/(3N)=1/3)  margins_uniform=True  OK
  N= 2  D1=1/6  (1/(3N)=1/6)  margins_uniform=True  OK
  N= 3  D1=1/9  (1/(3N)=1/9)  margins_uniform=True  OK
  N= 4  D1=1/12  (1/(3N)=1/12)  margins_uniform=True  OK
  N= 5  D1=1/15  (1/(3N)=1/15)  margins_uniform=True  OK
  N= 6  D1=1/18  (1/(3N)=1/18)  margins_uniform=True  OK
  N= 7  D1=1/21  (1/(3N)=1/21)  margins_uniform=True  OK
  N= 8  D1=1/24  (1/(3N)=1/24)  margins_uniform=True  OK
  N= 9  D1=1/27  (1/(3N)=1/27)  margins_uniform=True  OK
  N=10  D1=1/30  (1/(3N)=1/30)  margins_uniform=True  OK
  N=11  D1=1/33  (1/(3N)=1/33)  margins_uniform=True  OK
  N=12  D1=1/36  (1/(3N)=1/36)  margins_uniform=True  OK
(2) random rational checkerboards A: cell estimate and Lemma 3.3(c) bound, exact
  M=2 N=3 rep=0: D1=0.135802  ||H-PH||=0.083333  ||PH-HB||=0.111111 (<= 1/N=0.333333)  margins=True  OK
  M=2 N=3 rep=1: D1=0.122394  ||H-PH||=0.016667  ||PH-HB||=0.111111 (<= 1/N=0.333333)  margins=True  OK
  M=2 N=3 rep=2: D1=0.108561  ||H-PH||=0.005556  ||PH-HB||=0.111111 (<= 1/N=0.333333)  margins=True  OK
  M=3 N=2 rep=0: D1=0.138546  ||H-PH||=0.148148  ||PH-HB||=0.166667 (<= 1/N=0.500000)  margins=True  OK
  M=3 N=2 rep=1: D1=0.161663  ||H-PH||=0.024691  ||PH-HB||=0.166667 (<= 1/N=0.500000)  margins=True  OK
  M=3 N=2 rep=2: D1=0.287209  ||H-PH||=0.222222  ||PH-HB||=0.166667 (<= 1/N=0.500000)  margins=True  OK
  M=3 N=5 rep=0: D1=0.132730  ||H-PH||=0.088889  ||PH-HB||=0.066667 (<= 1/N=0.200000)  margins=True  OK
  M=3 N=5 rep=1: D1=0.108181  ||H-PH||=0.057848  ||PH-HB||=0.066667 (<= 1/N=0.200000)  margins=True  OK
  M=3 N=5 rep=2: D1=0.094058  ||H-PH||=0.032099  ||PH-HB||=0.066667 (<= 1/N=0.200000)  margins=True  OK
  M=4 N=6 rep=0: D1=0.118735  ||H-PH||=0.079545  ||PH-HB||=0.055556 (<= 1/N=0.166667)  margins=True  OK
  M=4 N=6 rep=1: D1=0.080247  ||H-PH||=0.041667  ||PH-HB||=0.055556 (<= 1/N=0.166667)  margins=True  OK
  M=4 N=6 rep=2: D1=0.067901  ||H-PH||=0.041667  ||PH-HB||=0.055556 (<= 1/N=0.166667)  margins=True  OK
  M=5 N=3 rep=0: D1=0.148860  ||H-PH||=0.104883  ||PH-HB||=0.111111 (<= 1/N=0.333333)  margins=True  OK
  M=5 N=3 rep=1: D1=0.187480  ||H-PH||=0.136948  ||PH-HB||=0.111111 (<= 1/N=0.333333)  margins=True  OK
  M=5 N=3 rep=2: D1=0.284361  ||H-PH||=0.211333  ||PH-HB||=0.111111 (<= 1/N=0.333333)  margins=True  OK
  M=6 N=4 rep=0: D1=0.164902  ||H-PH||=0.157937  ||PH-HB||=0.083333 (<= 1/N=0.250000)  margins=True  OK
  M=6 N=4 rep=1: D1=0.144786  ||H-PH||=0.115385  ||PH-HB||=0.083333 (<= 1/N=0.250000)  margins=True  OK
  M=6 N=4 rep=2: D1=0.226129  ||H-PH||=0.209402  ||PH-HB||=0.083333 (<= 1/N=0.250000)  margins=True  OK
  M=4 N=4 rep=0: D1=0.083333  ||H-PH||=0.000000  ||PH-HB||=0.083333 (<= 1/N=0.250000)  margins=True  OK
  M=4 N=4 rep=1: D1=0.083333  ||H-PH||=0.000000  ||PH-HB||=0.083333 (<= 1/N=0.250000)  margins=True  OK
  M=4 N=4 rep=2: D1=0.083333  ||H-PH||=0.000000  ||PH-HB||=0.083333 (<= 1/N=0.250000)  margins=True  OK
  M=2 N=7 rep=0: D1=0.071914  ||H-PH||=0.035714  ||PH-HB||=0.047619 (<= 1/N=0.142857)  margins=True  OK
  M=2 N=7 rep=1: D1=0.081633  ||H-PH||=0.035714  ||PH-HB||=0.047619 (<= 1/N=0.142857)  margins=True  OK
  M=2 N=7 rep=2: D1=0.081633  ||H-PH||=0.035714  ||PH-HB||=0.047619 (<= 1/N=0.142857)  margins=True  OK
  M=7 N=2 rep=0: D1=0.242520  ||H-PH||=0.203831  ||PH-HB||=0.166667 (<= 1/N=0.500000)  margins=True  OK
  M=7 N=2 rep=1: D1=0.239375  ||H-PH||=0.213648  ||PH-HB||=0.166667 (<= 1/N=0.500000)  margins=True  OK
  M=7 N=2 rep=2: D1=0.241348  ||H-PH||=0.214723  ||PH-HB||=0.166667 (<= 1/N=0.500000)  margins=True  OK
  M=5 N=8 rep=0: D1=0.113025  ||H-PH||=0.087722  ||PH-HB||=0.041667 (<= 1/N=0.125000)  margins=True  OK
  M=5 N=8 rep=1: D1=0.060674  ||H-PH||=0.034771  ||PH-HB||=0.041667 (<= 1/N=0.125000)  margins=True  OK
  M=5 N=8 rep=2: D1=0.095267  ||H-PH||=0.062581  ||PH-HB||=0.041667 (<= 1/N=0.125000)  margins=True  OK
  M=8 N=5 rep=0: D1=0.192552  ||H-PH||=0.179948  ||PH-HB||=0.066667 (<= 1/N=0.200000)  margins=True  OK
  M=8 N=5 rep=1: D1=0.188275  ||H-PH||=0.144103  ||PH-HB||=0.066667 (<= 1/N=0.200000)  margins=True  OK
  M=8 N=5 rep=2: D1=0.194464  ||H-PH||=0.188079  ||PH-HB||=0.066667 (<= 1/N=0.200000)  margins=True  OK
  M=6 N=9 rep=0: D1=0.093879  ||H-PH||=0.064815  ||PH-HB||=0.037037 (<= 1/N=0.111111)  margins=True  OK
  M=6 N=9 rep=1: D1=0.071161  ||H-PH||=0.041669  ||PH-HB||=0.037037 (<= 1/N=0.111111)  margins=True  OK
  M=6 N=9 rep=2: D1=0.089249  ||H-PH||=0.064815  ||PH-HB||=0.037037 (<= 1/N=0.111111)  margins=True  OK
  max over cases of N*||P_N H_A - H_BN||_1 = 0.333333 (claim: <= 1)
(3) Lemma 3.1, d = 2: d_inf^2 <= 8 D_1 on random checkerboard pairs (exact)
  195 pairs, max d_inf^2 / D_1 = 0.5000 (claim: <= 8)
ALL CHECKS PASSED
