== Pi3  (d = 3; bound = ||H_A - P_N H_A||_1 + 2/N)
N= 1  D_1=0.3166667 (resolutions differ by 1.1e-16)  N*D_1=0.31667  ||H-P_N H||=0.000000  bound=2.00000  OK
N= 2  D_1=0.1521302 (resolutions differ by 5.5e-07)  N*D_1=0.30426  ||H-P_N H||=0.000000  bound=1.00000  OK
N= 4  D_1=0.0751508 (resolutions differ by 3.8e-07)  N*D_1=0.30060  ||H-P_N H||=0.000000  bound=0.50000  OK
N= 8  D_1=0.0374494 (resolutions differ by 9.6e-08)  N*D_1=0.29960  ||H-P_N H||=0.000000  bound=0.25000  OK
N=16  D_1=0.0187081 (resolutions differ by 8.2e-08)  N*D_1=0.29933  ||H-P_N H||=0.000000  bound=0.12500  OK
N=32  D_1=0.0093519 (resolutions differ by 1.0e-07)  N*D_1=0.29926  ||H-P_N H||=0.000000  bound=0.06250  OK
== FGM3  (d = 3; bound = ||H_A - P_N H_A||_1 + 2/N)
N= 1  D_1=0.3111111 (resolutions differ by 5.6e-17)  N*D_1=0.31111  ||H-P_N H||=0.006944  bound=2.00694  OK
N= 2  D_1=0.1492930 (resolutions differ by 1.3e-07)  N*D_1=0.29859  ||H-P_N H||=0.003472  bound=1.00347  OK
N= 4  D_1=0.0737557 (resolutions differ by 5.0e-07)  N*D_1=0.29502  ||H-P_N H||=0.001736  bound=0.50174  OK
N= 8  D_1=0.0367570 (resolutions differ by 2.9e-08)  N*D_1=0.29406  ||H-P_N H||=0.000868  bound=0.25087  OK
N=16  D_1=0.0183627 (resolutions differ by 6.3e-08)  N*D_1=0.29380  ||H-P_N H||=0.000434  bound=0.12543  OK
N=32  D_1=0.0091793 (resolutions differ by 9.4e-08)  N*D_1=0.29374  ||H-P_N H||=0.000217  bound=0.06272  OK
== MixM3Pi3  (d = 3; bound = ||H_A - P_N H_A||_1 + 2/N)
N= 1  D_1=0.1583333 (resolutions differ by 8.3e-17)  N*D_1=0.15833  ||H-P_N H||=0.166667  bound=2.16667  OK
N= 2  D_1=0.0760651 (resolutions differ by 2.8e-07)  N*D_1=0.15213  ||H-P_N H||=0.083333  bound=1.08333  OK
N= 4  D_1=0.0375754 (resolutions differ by 1.9e-07)  N*D_1=0.15030  ||H-P_N H||=0.041667  bound=0.54167  OK
N= 8  D_1=0.0187247 (resolutions differ by 4.8e-08)  N*D_1=0.14980  ||H-P_N H||=0.020833  bound=0.27083  OK
N=16  D_1=0.0093541 (resolutions differ by 4.1e-08)  N*D_1=0.14966  ||H-P_N H||=0.010417  bound=0.13542  OK
N=32  D_1=0.0046760 (resolutions differ by 5.1e-08)  N*D_1=0.14963  ||H-P_N H||=0.005208  bound=0.06771  OK
== reference checks
D_1(Pi3, B_1 = M3) = 0.3166667 vs exact 19/60 = 0.3166667
N= 1: D_1((M3+Pi3)/2, B_N) = 0.1583333 vs D_1(Pi3,B_N)/2 = 0.1583333 (linearity, B_N(M3) = M3)
N= 2: D_1((M3+Pi3)/2, B_N) = 0.0760651 vs D_1(Pi3,B_N)/2 = 0.0760651 (linearity, B_N(M3) = M3)
N= 4: D_1((M3+Pi3)/2, B_N) = 0.0375754 vs D_1(Pi3,B_N)/2 = 0.0375754 (linearity, B_N(M3) = M3)
N= 8: D_1((M3+Pi3)/2, B_N) = 0.0187247 vs D_1(Pi3,B_N)/2 = 0.0187247 (linearity, B_N(M3) = M3)
N=16: D_1((M3+Pi3)/2, B_N) = 0.0093541 vs D_1(Pi3,B_N)/2 = 0.0093541 (linearity, B_N(M3) = M3)
N=32: D_1((M3+Pi3)/2, B_N) = 0.0046760 vs D_1(Pi3,B_N)/2 = 0.0046760 (linearity, B_N(M3) = M3)
