Second independent verification run: d = 3 and Proposition 5.1 (numpy 2.5.2 )

(A)+(B) random 3-dimensional rational checkerboards A against B_N(A)
  M=2 N=3: D_1(A,B_N)=0.12164  ||H_A-P_N H_A||_1=0.07143  ||P_N H_A-H_B||_1=0.10445 (N times it: 0.3134)  max_x cell term * N/2 = 0.3440  [G-change 2.3e-04]  ok
  M=3 N=2: D_1(A,B_N)=0.20758  ||H_A-P_N H_A||_1=0.09774  ||P_N H_A-H_B||_1=0.15692 (N times it: 0.3138)  max_x cell term * N/2 = 0.3204  [G-change 2.7e-04]  ok
  M=3 N=4: D_1(A,B_N)=0.10207  ||H_A-P_N H_A||_1=0.05458  ||P_N H_A-H_B||_1=0.07910 (N times it: 0.3164)  max_x cell term * N/2 = 0.3497  [G-change 5.9e-04]  ok
  M=4 N=3: D_1(A,B_N)=0.11772  ||H_A-P_N H_A||_1=0.05324  ||P_N H_A-H_B||_1=0.10378 (N times it: 0.3114)  max_x cell term * N/2 = 0.3053  [G-change 8.4e-05]  ok
  M=2 N=5: D_1(A,B_N)=0.06324  ||H_A-P_N H_A||_1=0.00000  ||P_N H_A-H_B||_1=0.06324 (N times it: 0.3162)  max_x cell term * N/2 = 0.2535  [G-change 2.9e-04]  ok
  M=5 N=2: D_1(A,B_N)=0.15786  ||H_A-P_N H_A||_1=0.11372  ||P_N H_A-H_B||_1=0.15466 (N times it: 0.3093)  max_x cell term * N/2 = 0.3627  [G-change 1.4e-04]  ok
  M=4 N=6: D_1(A,B_N)=0.06601  ||H_A-P_N H_A||_1=0.02431  ||P_N H_A-H_B||_1=0.05149 (N times it: 0.3089)  max_x cell term * N/2 = 0.2993  [G-change 1.1e-04]  ok
  M=6 N=4: D_1(A,B_N)=0.12965  ||H_A-P_N H_A||_1=0.09825  ||P_N H_A-H_B||_1=0.07947 (N times it: 0.3179)  max_x cell term * N/2 = 0.2906  [G-change 2.2e-04]  ok
  M=3 N=3: D_1(A,B_N)=0.10909  ||H_A-P_N H_A||_1=0.00000  ||P_N H_A-H_B||_1=0.10909 (N times it: 0.3273)  max_x cell term * N/2 = 0.3582  [G-change 2.8e-04]  ok
  M=5 N=7: D_1(A,B_N)=0.05949  ||H_A-P_N H_A||_1=0.03029  ||P_N H_A-H_B||_1=0.04450 (N times it: 0.3115)  max_x cell term * N/2 = 0.3221  [G-change 7.0e-05]  ok
  M=6 N=8: D_1(A,B_N)=0.06947  ||H_A-P_N H_A||_1=0.04558  ||P_N H_A-H_B||_1=0.03936 (N times it: 0.3148)  max_x cell term * N/2 = 0.2936  [G-change 8.0e-05]  ok
  M=4 N=1: D_1(A,B_N)=0.35607  ||H_A-P_N H_A||_1=0.12215  ||P_N H_A-H_B||_1=0.30492 (N times it: 0.3049)  max_x cell term * N/2 = 0.3832  [G-change 1.9e-04]  ok
  12 cases; largest (cell term at a single x)/(2/N) = 0.3832; largest D_1/(bound) = 0.2350

(C) A = Pi_3
  N=1: D_1(Pi_3, B_N) = 0.316630, N*D_1 = 0.3166, bound 2/N = 2.0000 (exact 19/60 = 0.316667; ok)
  N=2: D_1(Pi_3, B_N) = 0.152235, N*D_1 = 0.3045, bound 2/N = 1.0000 
  N=3: D_1(Pi_3, B_N) = 0.100515, N*D_1 = 0.3015, bound 2/N = 0.6667 
  N=4: D_1(Pi_3, B_N) = 0.074610, N*D_1 = 0.2984, bound 2/N = 0.5000 
  N=6: D_1(Pi_3, B_N) = 0.050018, N*D_1 = 0.3001, bound 2/N = 0.3333 
  N=8: D_1(Pi_3, B_N) = 0.037566, N*D_1 = 0.3005, bound 2/N = 0.2500 

(D) Lemma 3.1 for d = 3: d_inf^3 <= 128 D_1
  32 pairs; largest d_inf^3 / D_1 = 0.5378 (bound 128)

(E) Proposition 5.1: L <= d_inf and d_inf^{d+1} <= 2 (4d)^d L
  d = 2: 40 pairs, largest d_inf^3 / L = 0.7656 (bound 128)
  d = 3: 18 pairs, largest d_inf^4 / L = 0.4030 (bound 3456)

TOTAL failures: 0   (time 7 s)
