== (1)-(3) Kim's dyadic approximant (translations) equals the claim's B_N, exactly
OK   checkerboard M=3           N= 2: Birkhoff terms= 2, D_1(Kim R_n, B_N) = 0, cdf equal on grid+20 pts, cell masses equal
OK   checkerboard M=3           N= 4: Birkhoff terms= 6, D_1(Kim R_n, B_N) = 0, cdf equal on grid+20 pts, cell masses equal
OK   checkerboard M=3           N= 8: Birkhoff terms=21, D_1(Kim R_n, B_N) = 0, cdf equal on grid+20 pts, cell masses equal
OK   checkerboard M=5           N= 2: Birkhoff terms= 2, D_1(Kim R_n, B_N) = 0, cdf equal on grid+20 pts, cell masses equal
OK   checkerboard M=5           N= 4: Birkhoff terms= 9, D_1(Kim R_n, B_N) = 0, cdf equal on grid+20 pts, cell masses equal
OK   checkerboard M=5           N= 8: Birkhoff terms=28, D_1(Kim R_n, B_N) = 0, cdf equal on grid+20 pts, cell masses equal
OK   checkerboard M=6           N= 2: Birkhoff terms= 2, D_1(Kim R_n, B_N) = 0, cdf equal on grid+20 pts, cell masses equal
OK   checkerboard M=6           N= 4: Birkhoff terms= 8, D_1(Kim R_n, B_N) = 0, cdf equal on grid+20 pts, cell masses equal
OK   checkerboard M=6           N= 8: Birkhoff terms=30, D_1(Kim R_n, B_N) = 0, cdf equal on grid+20 pts, cell masses equal
OK   shuffle n=5                N= 2: Birkhoff terms= 2, D_1(Kim R_n, B_N) = 0, cdf equal on grid+20 pts, cell masses equal
OK   shuffle n=5                N= 4: Birkhoff terms= 3, D_1(Kim R_n, B_N) = 0, cdf equal on grid+20 pts, cell masses equal
OK   shuffle n=5                N= 8: Birkhoff terms= 4, D_1(Kim R_n, B_N) = 0, cdf equal on grid+20 pts, cell masses equal
OK   (M+Pi)/2                   N= 2: Birkhoff terms= 2, D_1(Kim R_n, B_N) = 0, cdf equal on grid+20 pts, cell masses equal
OK   (M+Pi)/2                   N= 4: Birkhoff terms= 4, D_1(Kim R_n, B_N) = 0, cdf equal on grid+20 pts, cell masses equal
OK   (M+Pi)/2                   N= 8: Birkhoff terms=11, D_1(Kim R_n, B_N) = 0, cdf equal on grid+20 pts, cell masses equal
OK   (W+checkerboard M=3)/2     N= 2: Birkhoff terms= 2, D_1(Kim R_n, B_N) = 0, cdf equal on grid+20 pts, cell masses equal
OK   (W+checkerboard M=3)/2     N= 4: Birkhoff terms= 8, D_1(Kim R_n, B_N) = 0, cdf equal on grid+20 pts, cell masses equal
OK   (W+checkerboard M=3)/2     N= 8: Birkhoff terms=29, D_1(Kim R_n, B_N) = 0, cdf equal on grid+20 pts, cell masses equal
== (4) both directions shrink (Kim: R_n -> T and R_n^* -> T^* strongly)
OK   checkerboard M=3       D_1(A,B_N) / D_1(A^t,B_N(A^t)): N=2: 0.21652 / 0.21652; N=4: 0.13713 / 0.13713; N=8: 0.07683 / 0.07683; N=16: 0.04056 / 0.04056
OK   checkerboard M=5       D_1(A,B_N) / D_1(A^t,B_N(A^t)): N=2: 0.20943 / 0.20148; N=4: 0.17410 / 0.13259; N=8: 0.09463 / 0.07427; N=16: 0.05215 / 0.03816
OK   checkerboard M=6       D_1(A,B_N) / D_1(A^t,B_N(A^t)): N=2: 0.25420 / 0.20835; N=4: 0.14126 / 0.13955; N=8: 0.07419 / 0.08155; N=16: 0.03928 / 0.04398
== (5) deliberately wrong inputs
OK   weights of two Birkhoff terms swapped (N=4): D_1 = 3/80 > 0 -> DETECTED (cell masses equal: False)
OK   anti-diagonal pieces (N=4): same cell masses, D_1 = 1/8 > 0 -> DETECTED
OK   weights of two Birkhoff terms swapped (N=8): D_1 = 3/1280 > 0 -> DETECTED (cell masses equal: False)
OK   anti-diagonal pieces (N=8): same cell masses, D_1 = 1/16 > 0 -> DETECTED
== failures: 0   (time 1.8 s)
