=== D1_L32: |X|=32, ell_0=2.664062, ell2_0/|X|=1.436096e+00 (M) highest state = -(lowest, mirrored signs): |diff| = 0.00e+00 (A) eigenvalue weight difference vs (3.7), 4 pairs x 16 states: max relative error 3.53e-08 (density-normalized 2.35e-09) (B) density vs exact form (3.3): max |X|*|diff| = 4.88e-14 (C) cost vs exact root (3.2): max |diff| = 5.61e-16 (D) cost minus 2nd-order (3.5): slope in gamma = 2.981 (E) eigenvalue weight minus 2nd-order (3.8): slope = 2.953; devs [7.43391052e-09 5.86500081e-08 4.56107826e-07 3.44613912e-06] (H) density weight minus F C + F2 C^2 + F3 C^3 (3.13): slope = 3.870 (F) ring: Theta_D - Theta(7.6): max |diff| = 2.11e-15 (I) single level: |B| slope fg 0.976, (a) 1.001; |B - B_1st| slope fg 1.924 (3 largest gamma 1.901), (a) 1.953; max |B - B_1st|/chi^2: fg 0.307, (a) 0.718 (J) relative error of the predicted difference breaks at the smallest gamma [full grip, (a)]: branch1.0: 5.0e-04, 1.1e-03, branch1.5: 2.2e-04, 3.8e-04, level: 3.8e-03, 1.3e-02 ... and at the largest gamma: branch1.0: 1.2e-03, 3.5e-03, branch1.5: 2.8e-03, 7.8e-03, level: 2.7e-02, 9.4e-02 (T) coupling (a), nu = gamma n: nu=-0.5: max |B-B_1st(nu)|/(chi^2(1+|nu/(1+nu)|)^2) = 0.66, slope 1.95, |B-B_1st(0)|/|B-B_1st(nu)| >= 5; nu=1.0: max |B-B_1st(nu)|/(chi^2(1+|nu/(1+nu)|)^2) = 0.40, slope 1.98, |B-B_1st(0)|/|B-B_1st(nu)| >= 7; nu=4.0: max |B-B_1st(nu)|/(chi^2(1+|nu/(1+nu)|)^2) = 0.24, slope 1.99, |B-B_1st(0)|/|B-B_1st(nu)| >= 13; nu=20.0: max |B-B_1st(nu)|/(chi^2(1+|nu/(1+nu)|)^2) = 0.17, slope 1.99, |B-B_1st(0)|/|B-B_1st(nu)| >= 18 nu=-1 (N_f=6394): Cost_+ = -3.04828e-02, Cost_- = -2.95257e-02, -ell_0 M^2/(n t_f) = -2.99988e-02; dW/Cost: + -2.0118e+01, - 2.0500e+01 === D1_L64: |X|=64, ell_0=5.332031, ell2_0/|X|=5.702774e+00 (M) highest state = -(lowest, mirrored signs): |diff| = 0.00e+00 (A) eigenvalue weight difference vs (3.7), 4 pairs x 16 states: max relative error 6.78e-08 (density-normalized 5.23e-09) (B) density vs exact form (3.3): max |X|*|diff| = 1.04e-13 (C) cost vs exact root (3.2): max |diff| = 8.20e-16 (D) cost minus 2nd-order (3.5): slope in gamma = 2.981 (E) eigenvalue weight minus 2nd-order (3.8): slope = 2.999; devs [2.52588374e-08 2.02053407e-07 1.61621885e-06 1.29029016e-05] (H) density weight minus F C + F2 C^2 + F3 C^3 (3.13): slope = 3.871 (F) ring: Theta_D - Theta(7.6): max |diff| = 5.00e-16 (I) single level: |B| slope fg 0.976, (a) 0.979; |B - B_1st| slope fg 1.951 (3 largest gamma 1.936), (a) 1.999; max |B - B_1st|/chi^2: fg 0.287, (a) 0.686 (J) relative error of the predicted difference breaks at the smallest gamma [full grip, (a)]: branch1.0: 6.3e-04, 1.3e-03, branch1.5: 3.7e-04, 6.3e-04, level: 3.9e-03, 7.9e-03 ... and at the largest gamma: branch1.0: 1.2e-03, 3.2e-03, branch1.5: 2.7e-03, 7.3e-03, level: 3.1e-02, 6.3e-02 (T) coupling (a), nu = gamma n: nu=-0.5: max |B-B_1st(nu)|/(chi^2(1+|nu/(1+nu)|)^2) = 1.01, slope 1.95, |B-B_1st(0)|/|B-B_1st(nu)| >= 4; nu=1.0: max |B-B_1st(nu)|/(chi^2(1+|nu/(1+nu)|)^2) = 0.40, slope 1.98, |B-B_1st(0)|/|B-B_1st(nu)| >= 8; nu=4.0: max |B-B_1st(nu)|/(chi^2(1+|nu/(1+nu)|)^2) = 0.24, slope 1.99, |B-B_1st(0)|/|B-B_1st(nu)| >= 13; nu=20.0: max |B-B_1st(nu)|/(chi^2(1+|nu/(1+nu)|)^2) = 0.17, slope 1.99, |B-B_1st(0)|/|B-B_1st(nu)| >= 19 nu=-1 (N_f=25594): Cost_+ = -3.04848e-02, Cost_- = -2.95255e-02, -ell_0 M^2/(n t_f) = -2.99997e-02; dW/Cost: + -6.5962e+02, - 6.5289e+02 === D2_L12: |X|=144, ell_0=0.444054, ell2_0/|X|=4.236694e-03 (M) highest state = -(lowest, mirrored signs): |diff| = 0.00e+00 (A) eigenvalue weight difference vs (3.7), 4 pairs x 16 states: max relative error 1.10e-07 (density-normalized 3.46e-10) (B) density vs exact form (3.3): max |X|*|diff| = 2.36e-14 (C) cost vs exact root (3.2): max |diff| = 2.45e-15 (D) cost minus 2nd-order (3.5): slope in gamma = 2.969 (E) eigenvalue weight minus 2nd-order (3.8): slope = 2.972; devs [1.12401601e-09 8.91675459e-09 7.01426045e-08 5.42886311e-07] (H) density weight minus F C + F2 C^2 + F3 C^3 (3.13): slope = 3.879 (I) single level: |B| slope fg 0.967, (a) 0.970; |B - B_1st| slope fg 1.936 (3 largest gamma 1.920), (a) 1.972; max |B - B_1st|/chi^2: fg 0.028, (a) 0.948 (J) relative error of the predicted difference breaks at the smallest gamma [full grip, (a)]: branch1.0: 5.1e-03, 1.9e-03, branch1.5: 1.1e-03, 3.1e-04, level: 1.8e-03, 1.1e-02 ... and at the largest gamma: branch1.0: 2.7e-03, 2.0e-03, branch1.5: 6.0e-03, 4.4e-03, level: 1.3e-02, 8.6e-02 (T) coupling (a), nu = gamma n: nu=-0.5: max |B-B_1st(nu)|/(chi^2(1+|nu/(1+nu)|)^2) = 1.13, slope 1.94, |B-B_1st(0)|/|B-B_1st(nu)| >= 3; nu=1.0: max |B-B_1st(nu)|/(chi^2(1+|nu/(1+nu)|)^2) = 0.07, slope 2.00, |B-B_1st(0)|/|B-B_1st(nu)| >= 39; nu=4.0: max |B-B_1st(nu)|/(chi^2(1+|nu/(1+nu)|)^2) = 0.06, slope 1.96, |B-B_1st(0)|/|B-B_1st(nu)| >= 55; nu=20.0: max |B-B_1st(nu)|/(chi^2(1+|nu/(1+nu)|)^2) = 0.05, slope 1.97, |B-B_1st(0)|/|B-B_1st(nu)| >= 63 nu=-1 (N_f=4796): Cost_+ = -3.05971e-02, Cost_- = -2.94226e-02, -ell_0 M^2/(n t_f) = -2.99986e-02; dW/Cost: + 4.4583e+00, - -4.4844e+00 === D2_L20: |X|=400, ell_0=0.525479, ell2_0/|X|=4.025398e-03 (M) highest state = -(lowest, mirrored signs): |diff| = 0.00e+00 (A) eigenvalue weight difference vs (3.7), 4 pairs x 16 states: max relative error 2.24e-07 (density-normalized 1.41e-09) (B) density vs exact form (3.3): max |X|*|diff| = 9.97e-14 (C) cost vs exact root (3.2): max |diff| = 3.30e-15 (D) cost minus 2nd-order (3.5): slope in gamma = 2.969 (E) eigenvalue weight minus 2nd-order (3.8): slope = 2.968; devs [9.82726264e-10 7.78323421e-09 6.10767640e-08 4.70655712e-07] (H) density weight minus F C + F2 C^2 + F3 C^3 (3.13): slope = 3.880 (I) single level: |B| slope fg 0.967, (a) 0.967; |B - B_1st| slope fg 1.944 (3 largest gamma 1.919), (a) 1.968; max |B - B_1st|/chi^2: fg 0.027, (a) 1.181 (J) relative error of the predicted difference breaks at the smallest gamma [full grip, (a)]: branch1.0: 1.0e-02, 2.2e-03, branch1.5: 2.1e-03, 4.8e-04, level: 2.3e-03, 1.3e-02 ... and at the largest gamma: branch1.0: 2.9e-03, 2.7e-03, branch1.5: 6.5e-03, 6.1e-03, level: 1.8e-02, 9.5e-02 (T) coupling (a), nu = gamma n: nu=-0.5: max |B-B_1st(nu)|/(chi^2(1+|nu/(1+nu)|)^2) = 1.23, slope 1.94, |B-B_1st(0)|/|B-B_1st(nu)| >= 3; nu=1.0: max |B-B_1st(nu)|/(chi^2(1+|nu/(1+nu)|)^2) = 0.15, slope 1.98, |B-B_1st(0)|/|B-B_1st(nu)| >= 19; nu=4.0: max |B-B_1st(nu)|/(chi^2(1+|nu/(1+nu)|)^2) = 0.04, slope 1.96, |B-B_1st(0)|/|B-B_1st(nu)| >= 82; nu=20.0: max |B-B_1st(nu)|/(chi^2(1+|nu/(1+nu)|)^2) = 0.04, slope 1.97, |B-B_1st(0)|/|B-B_1st(nu)| >= 87 nu=-1 (N_f=15764): Cost_+ = -3.06037e-02, Cost_- = -2.94207e-02, -ell_0 M^2/(n t_f) = -3.00007e-02; dW/Cost: + -9.5990e+00, - 9.5695e+00 === D3_L8: |X|=512, ell_0=0.224606, ell2_0/|X|=1.858469e-04 (M) highest state = -(lowest, mirrored signs): |diff| = 0.00e+00 (A) eigenvalue weight difference vs (3.7), 4 pairs x 16 states: max relative error 3.69e-07 (density-normalized 2.05e-09) (B) density vs exact form (3.3): max |X|*|diff| = 2.26e-14 (C) cost vs exact root (3.2): max |diff| = 3.83e-15 (D) cost minus 2nd-order (3.5): slope in gamma = 2.968 (E) eigenvalue weight minus 2nd-order (3.8): slope = 2.966; devs [1.14005289e-09 9.03096968e-09 7.07388019e-08 5.43167779e-07] (H) density weight minus F C + F2 C^2 + F3 C^3 (3.13): slope = 3.875 (I) single level: |B| slope fg 0.969, (a) 0.965; |B - B_1st| slope fg 1.816 (3 largest gamma 1.907), (a) 1.965; max |B - B_1st|/chi^2: fg 0.011, (a) 1.380 (J) relative error of the predicted difference breaks at the smallest gamma [full grip, (a)]: branch1.0: 1.6e-02, 3.4e-03, branch1.5: 7.9e-03, 1.6e-03, level: 7.6e-04, 1.4e-02 ... and at the largest gamma: branch1.0: 2.5e-03, 3.3e-03, branch1.5: 5.7e-03, 7.5e-03, level: 4.2e-03, 1.0e-01 (T) coupling (a), nu = gamma n: nu=-0.5: max |B-B_1st(nu)|/(chi^2(1+|nu/(1+nu)|)^2) = 1.31, slope 1.94, |B-B_1st(0)|/|B-B_1st(nu)| >= 2; nu=1.0: max |B-B_1st(nu)|/(chi^2(1+|nu/(1+nu)|)^2) = 0.21, slope 1.98, |B-B_1st(0)|/|B-B_1st(nu)| >= 13; nu=4.0: max |B-B_1st(nu)|/(chi^2(1+|nu/(1+nu)|)^2) = 0.06, slope 1.98, |B-B_1st(0)|/|B-B_1st(nu)| >= 48; nu=20.0: max |B-B_1st(nu)|/(chi^2(1+|nu/(1+nu)|)^2) = 0.04, slope 1.97, |B-B_1st(0)|/|B-B_1st(nu)| >= 80 nu=-1 (N_f=8625): Cost_+ = -3.06094e-02, Cost_- = -2.94134e-02, -ell_0 M^2/(n t_f) = -2.99995e-02; dW/Cost: + 1.2414e+00, - -1.2424e+00 === D3_L12: |X|=1728, ell_0=0.233942, ell2_0/|X|=7.996514e-05 (M) highest state = -(lowest, mirrored signs): |diff| = 0.00e+00 (A) eigenvalue weight difference vs (3.7), 4 pairs x 16 states: max relative error 7.07e-07 (density-normalized 1.42e-09) (B) density vs exact form (3.3): max |X|*|diff| = 3.18e-15 (C) cost vs exact root (3.2): max |diff| = 1.10e-14 (D) cost minus 2nd-order (3.5): slope in gamma = 2.968 (E) eigenvalue weight minus 2nd-order (3.8): slope = 2.967; devs [1.94909595e-10 1.54553921e-09 1.21125117e-08 9.31082265e-08] (H) density weight minus F C + F2 C^2 + F3 C^3 (3.13): slope = 4.003 (I) single level: |B| slope fg 0.969, (a) 0.966; |B - B_1st| slope fg 1.610 (3 largest gamma 1.918), (a) 1.967; max |B - B_1st|/chi^2: fg 0.018, (a) 1.258 (J) relative error of the predicted difference breaks at the smallest gamma [full grip, (a)]: branch1.0: 9.4e-02, 1.2e-02, branch1.5: 8.6e-03, 1.2e-03, level: 5.4e-04, 1.3e-02 ... and at the largest gamma: branch1.0: 2.5e-03, 3.2e-03, branch1.5: 5.9e-03, 7.2e-03, level: 2.8e-03, 9.9e-02 (T) coupling (a), nu = gamma n: nu=-0.5: max |B-B_1st(nu)|/(chi^2(1+|nu/(1+nu)|)^2) = 1.26, slope 1.94, |B-B_1st(0)|/|B-B_1st(nu)| >= 2; nu=1.0: max |B-B_1st(nu)|/(chi^2(1+|nu/(1+nu)|)^2) = 0.17, slope 1.98, |B-B_1st(0)|/|B-B_1st(nu)| >= 15; nu=4.0: max |B-B_1st(nu)|/(chi^2(1+|nu/(1+nu)|)^2) = 0.04, slope 1.98, |B-B_1st(0)|/|B-B_1st(nu)| >= 71; nu=20.0: max |B-B_1st(nu)|/(chi^2(1+|nu/(1+nu)|)^2) = 0.02, slope 1.98, |B-B_1st(0)|/|B-B_1st(nu)| >= 135 nu=-1 (N_f=30319): Cost_+ = -3.06112e-02, Cost_- = -2.94125e-02, -ell_0 M^2/(n t_f) = -2.99999e-02; dW/Cost: + -2.2559e+00, - 2.2511e+00 (K) distance scan 1D, L=64 (r' = antipode, density): j, B_fg(num), B_fg(1st order), B_a(num), B_a(1st order), -(eta/2)(ell(r)+ell(r')) [fg], -(g_b/t_f)ell_0 [(a) far limit] s=+1 j= 1 2.5276e-03 2.9639e-03 -4.5645e-02 -4.6879e-02 -9.6938e-03 -5.0000e-02 s=+1 j= 2 5.3999e-03 5.8000e-03 -4.2911e-02 -4.3900e-02 -7.5667e-03 -5.0000e-02 s=+1 j= 3 8.1842e-03 8.5431e-03 -4.0260e-02 -4.1018e-02 -5.5094e-03 -5.0000e-02 s=+1 j= 4 1.0880e-02 1.1193e-02 -3.7694e-02 -3.8234e-02 -3.5218e-03 -5.0000e-02 s=+1 j= 5 1.3487e-02 1.3750e-02 -3.5212e-02 -3.5548e-02 -1.6040e-03 -5.0000e-02 s=+1 j= 6 1.6004e-02 1.6214e-02 -3.2816e-02 -3.2960e-02 2.4409e-04 -5.0000e-02 s=+1 j= 7 1.8430e-02 1.8586e-02 -3.0506e-02 -3.0469e-02 2.0224e-03 -5.0000e-02 s=+1 j= 8 2.0766e-02 2.0864e-02 -2.8283e-02 -2.8076e-02 3.7311e-03 -5.0000e-02 s=+1 j= 9 2.3011e-02 2.3049e-02 -2.6146e-02 -2.5780e-02 5.3699e-03 -5.0000e-02 s=+1 j=10 2.5164e-02 2.5141e-02 -2.4097e-02 -2.3582e-02 6.9391e-03 -5.0000e-02 s=+1 j=11 2.7224e-02 2.7140e-02 -2.2135e-02 -2.1482e-02 8.4385e-03 -5.0000e-02 s=+1 j=12 2.9192e-02 2.9046e-02 -2.0262e-02 -1.9480e-02 9.8681e-03 -5.0000e-02 s=+1 j=13 3.1066e-02 3.0860e-02 -1.8478e-02 -1.7575e-02 1.1228e-02 -5.0000e-02 s=+1 j=14 3.2847e-02 3.2580e-02 -1.6782e-02 -1.5768e-02 1.2518e-02 -5.0000e-02 s=+1 j=15 3.4534e-02 3.4207e-02 -1.5176e-02 -1.4059e-02 1.3739e-02 -5.0000e-02 s=+1 j=16 3.6127e-02 3.5741e-02 -1.3660e-02 -1.2447e-02 1.4889e-02 -5.0000e-02 s=+1 j=17 3.7624e-02 3.7183e-02 -1.2235e-02 -1.0933e-02 1.5970e-02 -5.0000e-02 s=+1 j=18 3.9027e-02 3.8531e-02 -1.0899e-02 -9.5165e-03 1.6982e-02 -5.0000e-02 s=+1 j=19 4.0335e-02 3.9786e-02 -9.6546e-03 -8.1978e-03 1.7923e-02 -5.0000e-02 s=+1 j=20 4.1546e-02 4.0949e-02 -8.5012e-03 -6.9768e-03 1.8795e-02 -5.0000e-02 s=+1 j=21 4.2662e-02 4.2018e-02 -7.4390e-03 -5.8535e-03 1.9597e-02 -5.0000e-02 s=+1 j=22 4.3682e-02 4.2994e-02 -6.4685e-03 -4.8278e-03 2.0329e-02 -5.0000e-02 s=+1 j=23 4.4605e-02 4.3878e-02 -5.5897e-03 -3.8999e-03 2.0992e-02 -5.0000e-02 s=+1 j=24 4.5431e-02 4.4668e-02 -4.8029e-03 -3.0696e-03 2.1584e-02 -5.0000e-02 s=+1 j=25 4.6161e-02 4.5365e-02 -4.1082e-03 -2.3370e-03 2.2107e-02 -5.0000e-02 s=+1 j=26 4.6794e-02 4.5970e-02 -3.5059e-03 -1.7021e-03 2.2561e-02 -5.0000e-02 s=+1 j=27 4.7329e-02 4.6481e-02 -2.9960e-03 -1.1648e-03 2.2944e-02 -5.0000e-02 s=+1 j=28 4.7768e-02 4.6900e-02 -2.5786e-03 -7.2528e-04 2.3258e-02 -5.0000e-02 s=+1 j=29 4.8109e-02 4.7225e-02 -2.2539e-03 -3.8340e-04 2.3502e-02 -5.0000e-02 s=+1 j=30 4.8353e-02 4.7458e-02 -2.0219e-03 -1.3920e-04 2.3677e-02 -5.0000e-02 s=+1 j=31 4.8499e-02 4.7597e-02 -1.8827e-03 7.3249e-06 2.3781e-02 -5.0000e-02 s=-1 j= 1 -3.7745e-03 -3.2756e-03 4.8077e-02 4.6879e-02 1.0713e-02 5.0000e-02 s=-1 j= 2 -6.8627e-03 -6.4100e-03 4.4828e-02 4.3900e-02 8.3625e-03 5.0000e-02 s=-1 j= 3 -9.8424e-03 -9.4415e-03 4.1693e-02 4.1018e-02 6.0888e-03 5.0000e-02 s=-1 j= 4 -1.2714e-02 -1.2370e-02 3.8672e-02 3.8234e-02 3.8922e-03 5.0000e-02 s=-1 j= 5 -1.5479e-02 -1.5196e-02 3.5763e-02 3.5548e-02 1.7727e-03 5.0000e-02 s=-1 j= 6 -1.8137e-02 -1.7920e-02 3.2967e-02 3.2960e-02 -2.6976e-04 5.0000e-02 s=-1 j= 7 -2.0690e-02 -2.0540e-02 3.0281e-02 3.0469e-02 -2.2351e-03 5.0000e-02 s=-1 j= 8 -2.3137e-02 -2.3058e-02 2.7706e-02 2.8076e-02 -4.1234e-03 5.0000e-02 s=-1 j= 9 -2.5480e-02 -2.5473e-02 2.5241e-02 2.5780e-02 -5.9347e-03 5.0000e-02 s=-1 j=10 -2.7719e-02 -2.7785e-02 2.2886e-02 2.3582e-02 -7.6688e-03 5.0000e-02 s=-1 j=11 -2.9855e-02 -2.9995e-02 2.0639e-02 2.1482e-02 -9.3259e-03 5.0000e-02 s=-1 j=12 -3.1888e-02 -3.2101e-02 1.8500e-02 1.9480e-02 -1.0906e-02 5.0000e-02 s=-1 j=13 -3.3818e-02 -3.4105e-02 1.6469e-02 1.7575e-02 -1.2409e-02 5.0000e-02 s=-1 j=14 -3.5647e-02 -3.6006e-02 1.4546e-02 1.5768e-02 -1.3835e-02 5.0000e-02 s=-1 j=15 -3.7374e-02 -3.7805e-02 1.2728e-02 1.4059e-02 -1.5184e-02 5.0000e-02 s=-1 j=16 -3.9001e-02 -3.9500e-02 1.1017e-02 1.2447e-02 -1.6455e-02 5.0000e-02 s=-1 j=17 -4.0526e-02 -4.1093e-02 9.4123e-03 1.0933e-02 -1.7650e-02 5.0000e-02 s=-1 j=18 -4.1952e-02 -4.2583e-02 7.9126e-03 9.5165e-03 -1.8767e-02 5.0000e-02 s=-1 j=19 -4.3278e-02 -4.3971e-02 6.5178e-03 8.1978e-03 -1.9808e-02 5.0000e-02 s=-1 j=20 -4.4504e-02 -4.5255e-02 5.2278e-03 6.9768e-03 -2.0771e-02 5.0000e-02 s=-1 j=21 -4.5631e-02 -4.6437e-02 4.0422e-03 5.8535e-03 -2.1658e-02 5.0000e-02 s=-1 j=22 -4.6659e-02 -4.7516e-02 2.9606e-03 4.8278e-03 -2.2467e-02 5.0000e-02 s=-1 j=23 -4.7588e-02 -4.8492e-02 1.9829e-03 3.8999e-03 -2.3199e-02 5.0000e-02 s=-1 j=24 -4.8419e-02 -4.9366e-02 1.1087e-03 3.0696e-03 -2.3854e-02 5.0000e-02 s=-1 j=25 -4.9152e-02 -5.0136e-02 3.3783e-04 2.3370e-03 -2.4432e-02 5.0000e-02 s=-1 j=26 -4.9787e-02 -5.0804e-02 -3.2984e-04 1.7021e-03 -2.4933e-02 5.0000e-02 s=-1 j=27 -5.0323e-02 -5.1370e-02 -8.9452e-04 1.1648e-03 -2.5357e-02 5.0000e-02 s=-1 j=28 -5.0762e-02 -5.1832e-02 -1.3563e-03 7.2528e-04 -2.5704e-02 5.0000e-02 s=-1 j=29 -5.1104e-02 -5.2192e-02 -1.7154e-03 3.8340e-04 -2.5974e-02 5.0000e-02 s=-1 j=30 -5.1347e-02 -5.2449e-02 -1.9718e-03 1.3920e-04 -2.6167e-02 5.0000e-02 s=-1 j=31 -5.1493e-02 -5.2603e-02 -2.1257e-03 -7.3249e-06 -2.6282e-02 5.0000e-02 (K) distance scan 2D, L=20 (r' = antipode, density): j, B_fg(num), B_fg(1st order), B_a(num), B_a(1st order), -(eta/2)(ell(r)+ell(r')) [fg], -(g_b/t_f)ell_0 [(a) far limit] s=+1 j= 1 -8.4978e-03 -8.4456e-03 -5.5733e-02 -5.8856e-02 -9.9924e-03 -5.0000e-02 s=+1 j= 2 -2.8846e-03 -2.8411e-03 -5.0387e-02 -5.2971e-02 -4.9406e-03 -5.0000e-02 s=+1 j= 3 4.8955e-04 5.2406e-04 -4.7174e-02 -4.9438e-02 -2.0532e-03 -5.0000e-02 s=+1 j= 4 2.8317e-03 2.8573e-03 -4.4943e-02 -4.6988e-02 -1.4103e-04 -5.0000e-02 s=+1 j= 5 4.5826e-03 4.5997e-03 -4.3275e-02 -4.5158e-02 1.2180e-03 -5.0000e-02 s=+1 j= 6 5.9393e-03 5.9485e-03 -4.1983e-02 -4.3742e-02 2.2061e-03 -5.0000e-02 s=+1 j= 7 7.0020e-03 7.0042e-03 -4.0971e-02 -4.2634e-02 2.9146e-03 -5.0000e-02 s=+1 j= 8 7.8122e-03 7.8084e-03 -4.0200e-02 -4.1789e-02 3.3937e-03 -5.0000e-02 s=+1 j= 9 8.3500e-03 8.3420e-03 -3.9688e-02 -4.1229e-02 3.6715e-03 -5.0000e-02 s=+1 j=10 8.5443e-03 8.5346e-03 -3.9503e-02 -4.1026e-02 3.7626e-03 -5.0000e-02 s=-1 j= 1 9.2705e-03 9.3346e-03 6.2334e-02 5.8856e-02 1.1044e-02 5.0000e-02 s=-1 j= 2 3.0870e-03 3.1401e-03 5.5825e-02 5.2971e-02 5.4607e-03 5.0000e-02 s=-1 j= 3 -6.2103e-04 -5.7922e-04 5.1922e-02 4.9438e-02 2.2693e-03 5.0000e-02 s=-1 j= 4 -3.1888e-03 -3.1580e-03 4.9220e-02 4.6988e-02 1.5587e-04 5.0000e-02 s=-1 j= 5 -5.1041e-03 -5.0838e-03 4.7204e-02 4.5158e-02 -1.3462e-03 5.0000e-02 s=-1 j= 6 -6.5852e-03 -6.5746e-03 4.5645e-02 4.3742e-02 -2.4384e-03 5.0000e-02 s=-1 j= 7 -7.7434e-03 -7.7414e-03 4.4425e-02 4.2634e-02 -3.2214e-03 5.0000e-02 s=-1 j= 8 -8.6250e-03 -8.6303e-03 4.3497e-02 4.1789e-02 -3.7509e-03 5.0000e-02 s=-1 j= 9 -9.2096e-03 -9.2200e-03 4.2882e-02 4.1229e-02 -4.0580e-03 5.0000e-02 s=-1 j=10 -9.4206e-03 -9.4330e-03 4.2660e-02 4.1026e-02 -4.1587e-03 5.0000e-02 (K) distance scan 3D, L=12 (r' = antipode, density): j, B_fg(num), B_fg(1st order), B_a(num), B_a(1st order), -(eta/2)(ell(r)+ell(r')) [fg], -(g_b/t_f)ell_0 [(a) far limit] s=+1 j= 1 -6.0983e-03 -6.0929e-03 -5.3424e-02 -5.6391e-02 -6.3037e-03 -5.0000e-02 s=+1 j= 2 -1.5676e-03 -1.5633e-03 -4.9110e-02 -5.1635e-02 -1.9403e-03 -5.0000e-02 s=+1 j= 3 1.0608e-04 1.0947e-04 -4.7516e-02 -4.9879e-02 -4.3436e-04 -5.0000e-02 s=+1 j= 4 9.1017e-04 9.1284e-04 -4.6750e-02 -4.9035e-02 2.1651e-04 -5.0000e-02 s=+1 j= 5 1.3332e-03 1.3354e-03 -4.6347e-02 -4.8592e-02 5.1213e-04 -5.0000e-02 s=+1 j= 6 1.4763e-03 1.4782e-03 -4.6211e-02 -4.8442e-02 5.9926e-04 -5.0000e-02 s=-1 j= 1 6.7276e-03 6.7342e-03 5.9702e-02 5.6391e-02 6.9672e-03 5.0000e-02 s=-1 j= 2 1.7226e-03 1.7279e-03 5.4434e-02 5.1635e-02 2.1446e-03 5.0000e-02 s=-1 j= 3 -1.2512e-04 -1.2099e-04 5.2489e-02 4.9879e-02 4.8009e-04 5.0000e-02 s=-1 j= 4 -1.0122e-03 -1.0089e-03 5.1555e-02 4.9035e-02 -2.3930e-04 5.0000e-02 s=-1 j= 5 -1.4786e-03 -1.4760e-03 5.1064e-02 4.8592e-02 -5.6604e-04 5.0000e-02 s=-1 j= 6 -1.6362e-03 -1.6338e-03 5.0898e-02 4.8442e-02 -6.6234e-04 5.0000e-02 === D3_L20: ell_0=0.241447 (K) distance scan 3D, L=20 (r' = antipode, density): j, B_fg(num), B_fg(1st order), B_a(num), B_a(1st order), -(eta/2)(ell(r)+ell(r')) [fg], -(g_b/t_f)ell_0 [(a) far limit] s=+1 j= 1 -6.9872e-03 -6.9853e-03 -5.4273e-02 -5.7333e-02 -7.0592e-03 -5.0000e-02 s=+1 j= 2 -2.6715e-03 -2.6699e-03 -5.0163e-02 -5.2802e-02 -2.8079e-03 -5.0000e-02 s=+1 j= 3 -1.1026e-03 -1.1012e-03 -4.8669e-02 -5.1155e-02 -1.3055e-03 -5.0000e-02 s=+1 j= 4 -3.4119e-04 -3.3992e-04 -4.7944e-02 -5.0356e-02 -6.0565e-04 -5.0000e-02 s=+1 j= 5 1.0698e-04 1.0808e-04 -4.7517e-02 -4.9885e-02 -2.1404e-04 -5.0000e-02 s=+1 j= 6 4.0166e-04 4.0261e-04 -4.7236e-02 -4.9576e-02 2.7876e-05 -5.0000e-02 s=+1 j= 7 6.0608e-04 6.0691e-04 -4.7042e-02 -4.9361e-02 1.8294e-04 -5.0000e-02 s=+1 j= 8 7.4717e-04 7.4789e-04 -4.6907e-02 -4.9213e-02 2.8014e-04 -5.0000e-02 s=+1 j= 9 8.3330e-04 8.3396e-04 -4.6825e-02 -4.9123e-02 3.3392e-04 -5.0000e-02 s=+1 j=10 8.6280e-04 8.6343e-04 -4.6797e-02 -4.9092e-02 3.5117e-04 -5.0000e-02 s=-1 j= 1 7.7183e-03 7.7206e-03 6.0753e-02 5.7333e-02 7.8022e-03 5.0000e-02 s=-1 j= 2 2.9489e-03 2.9509e-03 5.5733e-02 5.2802e-02 3.1034e-03 5.0000e-02 s=-1 j= 3 1.2153e-03 1.2171e-03 5.3908e-02 5.1155e-02 1.4429e-03 5.0000e-02 s=-1 j= 4 3.7416e-04 3.7571e-04 5.3023e-02 5.0356e-02 6.6940e-04 5.0000e-02 s=-1 j= 5 -1.2080e-04 -1.1946e-04 5.2502e-02 4.9885e-02 2.3657e-04 5.0000e-02 s=-1 j= 6 -4.4615e-04 -4.4499e-04 5.2159e-02 4.9576e-02 -3.0810e-05 5.0000e-02 s=-1 j= 7 -6.7180e-04 -6.7079e-04 5.1922e-02 4.9361e-02 -2.0219e-04 5.0000e-02 s=-1 j= 8 -8.2750e-04 -8.2662e-04 5.1758e-02 4.9213e-02 -3.0963e-04 5.0000e-02 s=-1 j= 9 -9.2255e-04 -9.2174e-04 5.1658e-02 4.9123e-02 -3.6907e-04 5.0000e-02 s=-1 j=10 -9.5509e-04 -9.5432e-04 5.1623e-02 4.9092e-02 -3.8813e-04 5.0000e-02 (K2) 1D L=128, r = j e1, r' = 2j e1, eigenvalue weights, max|g_b| ell_0/t_f = 0.03: M, s, j, B_fg num, 1st, (3.16); B_a num, 1st, (3.16); |num-1st|/chi^2 [fg, a]; |1st-(3.16)|/(|eta| e) [fg, a] M=1.0 s=+1 j= 2 -1.6187e-02 -1.6023e-02 -1.9608e-02 | -3.5552e-02 -3.6345e-02 -4.0002e-02 | 0.41 1.98 | 0.97 0.99 M=1.0 s=+1 j= 4 -1.2801e-02 -1.2634e-02 -1.9608e-02 | -3.2232e-02 -3.2887e-02 -4.0002e-02 | 0.42 1.64 | 0.95 0.97 M=1.0 s=+1 j= 8 -6.5829e-03 -6.4301e-03 -1.9608e-02 | -2.6137e-02 -2.6559e-02 -4.0002e-02 | 0.38 1.06 | 0.90 0.91 M=1.0 s=+1 j=16 3.6000e-03 3.6800e-03 -1.9608e-02 | -1.6154e-02 -1.6246e-02 -4.0002e-02 | 0.20 0.23 | 0.79 0.81 M=1.0 s=-1 j= 2 1.6500e-02 1.6677e-02 2.0408e-02 | 3.7158e-02 3.6345e-02 4.0002e-02 | 0.44 2.03 | 0.97 0.96 M=1.0 s=-1 j= 4 1.2970e-02 1.3150e-02 2.0408e-02 | 3.3557e-02 3.2887e-02 4.0002e-02 | 0.45 1.67 | 0.95 0.93 M=1.0 s=-1 j= 8 6.5292e-03 6.6925e-03 2.0408e-02 | 2.6985e-02 2.6559e-02 4.0002e-02 | 0.41 1.07 | 0.90 0.88 M=1.0 s=-1 j=16 -3.9140e-03 -3.8302e-03 2.0408e-02 | 1.6330e-02 1.6246e-02 4.0002e-02 | 0.21 0.21 | 0.79 0.78 M=1.5 s=+1 j= 2 -2.4161e-02 -2.3799e-02 -2.9123e-02 | -5.2746e-02 -5.4517e-02 -6.0003e-02 | 0.40 1.97 | 0.97 1.00 M=1.5 s=+1 j= 4 -1.9133e-02 -1.8765e-02 -2.9123e-02 | -4.7865e-02 -4.9331e-02 -6.0003e-02 | 0.41 1.63 | 0.95 0.98 M=1.5 s=+1 j= 8 -9.8889e-03 -9.5507e-03 -2.9123e-02 | -3.8891e-02 -3.9838e-02 -6.0003e-02 | 0.38 1.05 | 0.90 0.92 M=1.5 s=+1 j=16 5.2880e-03 5.4659e-03 -2.9123e-02 | -2.4159e-02 -2.4369e-02 -6.0003e-02 | 0.20 0.23 | 0.79 0.82 M=1.5 s=-1 j= 2 2.4864e-02 2.5271e-02 3.0924e-02 | 5.6360e-02 5.4517e-02 6.0003e-02 | 0.45 2.05 | 0.97 0.95 M=1.5 s=-1 j= 4 1.9514e-02 1.9926e-02 3.0924e-02 | 5.0846e-02 4.9331e-02 6.0003e-02 | 0.46 1.68 | 0.95 0.92 M=1.5 s=-1 j= 8 9.7673e-03 1.0141e-02 3.0924e-02 | 4.0799e-02 3.9838e-02 6.0003e-02 | 0.42 1.07 | 0.90 0.87 M=1.5 s=-1 j=16 -5.9946e-03 -5.8039e-03 3.0924e-02 | 2.4553e-02 2.4369e-02 6.0003e-02 | 0.21 0.20 | 0.79 0.77 (K2) 2D L=48, r = j e1, r' = 2j e1, eigenvalue weights, max|g_b| ell_0/t_f = 0.03: M, s, j, B_fg num, 1st, (3.16); B_a num, 1st, (3.16); |num-1st|/chi^2 [fg, a]; |1st-(3.16)|/(|eta| e) [fg, a] M=1.0 s=+1 j= 2 -7.1480e-03 -7.1406e-03 -7.1388e-03 | -2.6619e-02 -2.7283e-02 -2.7281e-02 | 0.02 1.66 | 0.00 0.00 M=1.0 s=+1 j= 3 -5.1527e-03 -5.1454e-03 -5.2357e-03 | -2.4663e-02 -2.5248e-02 -2.5340e-02 | 0.02 1.46 | 0.02 0.02 M=1.0 s=+1 j= 4 -3.7471e-03 -3.7401e-03 -3.8854e-03 | -2.3285e-02 -2.3815e-02 -2.3963e-02 | 0.02 1.33 | 0.04 0.04 M=1.0 s=+1 j= 6 -1.8085e-03 -1.8027e-03 -1.9823e-03 | -2.1384e-02 -2.1838e-02 -2.2022e-02 | 0.01 1.14 | 0.05 0.05 M=1.0 s=-1 j= 2 7.4240e-03 7.4321e-03 7.4301e-03 | 2.7980e-02 2.7283e-02 2.7281e-02 | 0.02 1.74 | 0.00 0.00 M=1.0 s=-1 j= 3 5.3478e-03 5.3554e-03 5.4494e-03 | 2.5861e-02 2.5248e-02 2.5340e-02 | 0.02 1.53 | 0.02 0.02 M=1.0 s=-1 j= 4 3.8859e-03 3.8928e-03 4.0440e-03 | 2.4369e-02 2.3815e-02 2.3963e-02 | 0.02 1.39 | 0.04 0.04 M=1.0 s=-1 j= 6 1.8700e-03 1.8762e-03 2.0632e-03 | 2.2312e-02 2.1838e-02 2.2022e-02 | 0.02 1.18 | 0.05 0.05 M=1.5 s=+1 j= 2 -1.0623e-02 -1.0607e-02 -1.0604e-02 | -3.9447e-02 -4.0925e-02 -4.0922e-02 | 0.02 1.64 | 0.00 0.00 M=1.5 s=+1 j= 3 -7.6587e-03 -7.6432e-03 -7.7772e-03 | -3.6569e-02 -3.7872e-02 -3.8010e-02 | 0.02 1.45 | 0.02 0.02 M=1.5 s=+1 j= 4 -5.5706e-03 -5.5557e-03 -5.7715e-03 | -3.4541e-02 -3.5722e-02 -3.5944e-02 | 0.02 1.31 | 0.04 0.05 M=1.5 s=+1 j= 6 -2.6908e-03 -2.6777e-03 -2.9445e-03 | -3.1745e-02 -3.2758e-02 -3.3033e-02 | 0.01 1.12 | 0.05 0.05 M=1.5 s=-1 j= 2 1.1245e-02 1.1263e-02 1.1260e-02 | 4.2511e-02 4.0925e-02 4.0922e-02 | 0.02 1.76 | 0.00 0.00 M=1.5 s=-1 j= 3 8.0982e-03 8.1159e-03 8.2583e-03 | 3.9267e-02 3.7872e-02 3.8010e-02 | 0.02 1.55 | 0.02 0.02 M=1.5 s=-1 j= 4 5.8822e-03 5.8994e-03 6.1285e-03 | 3.6983e-02 3.5722e-02 3.5944e-02 | 0.02 1.40 | 0.04 0.04 M=1.5 s=-1 j= 6 2.8284e-03 2.8433e-03 3.1267e-03 | 3.3835e-02 3.2758e-02 3.3033e-02 | 0.02 1.20 | 0.05 0.05 (K2) 3D L=32, r = j e1, r' = 2j e1, eigenvalue weights, max|g_b| ell_0/t_f = 0.03: M, s, j, B_fg num, 1st, (3.16); B_a num, 1st, (3.16); |num-1st|/chi^2 [fg, a]; |1st-(3.16)|/(|eta| e) [fg, a] M=1.0 s=+1 j= 2 -1.9537e-03 -1.9549e-03 -1.8186e-03 | -2.1523e-02 -2.1994e-02 -2.1855e-02 | 0.00 1.18 | 0.01 0.01 M=1.0 s=+1 j= 3 -1.0620e-03 -1.0635e-03 -1.0247e-03 | -2.0649e-02 -2.1085e-02 -2.1045e-02 | 0.00 1.09 | 0.01 0.01 M=1.0 s=+1 j= 4 -6.3324e-04 -6.3763e-04 -6.2772e-04 | -2.0229e-02 -2.0650e-02 -2.0640e-02 | 0.01 1.05 | 0.01 0.01 M=1.0 s=-1 j= 2 2.0352e-03 2.0347e-03 1.8928e-03 | 2.2485e-02 2.1994e-02 2.1855e-02 | 0.00 1.23 | 0.01 0.01 M=1.0 s=-1 j= 3 1.1023e-03 1.1070e-03 1.0665e-03 | 2.1533e-02 2.1085e-02 2.1045e-02 | 0.01 1.12 | 0.01 0.01 M=1.0 s=-1 j= 4 6.5866e-04 6.6366e-04 6.5334e-04 | 2.1080e-02 2.0650e-02 2.0640e-02 | 0.01 1.07 | 0.01 0.01 M=1.5 s=+1 j= 2 -2.9042e-03 -2.9039e-03 -2.7014e-03 | -3.1946e-02 -3.2991e-02 -3.2782e-02 | 0.00 1.16 | 0.01 0.01 M=1.5 s=+1 j= 3 -1.5836e-03 -1.5798e-03 -1.5221e-03 | -3.0664e-02 -3.1627e-02 -3.1568e-02 | 0.00 1.07 | 0.01 0.01 M=1.5 s=+1 j= 4 -9.3921e-04 -9.4716e-04 -9.3244e-04 | -3.0038e-02 -3.0975e-02 -3.0960e-02 | 0.01 1.04 | 0.01 0.01 M=1.5 s=-1 j= 2 3.0841e-03 3.0835e-03 2.8685e-03 | 3.4107e-02 3.2991e-02 3.2782e-02 | 0.00 1.24 | 0.01 0.01 M=1.5 s=-1 j= 3 1.6764e-03 1.6775e-03 1.6162e-03 | 3.2656e-02 3.1627e-02 3.1568e-02 | 0.00 1.14 | 0.01 0.01 M=1.5 s=-1 j= 4 9.9627e-04 1.0057e-03 9.9011e-04 | 3.1955e-02 3.0975e-02 3.0960e-02 | 0.01 1.09 | 0.01 0.01 (U) lattice sums: {"2D_L64_j2": {"T2*L^2/R^2": 1.1963, "T2*L^2/(R^2 ln(L/R))": 0.4315}, "2D_L64_j4": {"T2*L^2/R^2": 0.8549, "T2*L^2/(R^2 ln(L/R))": 0.4111}, "2D_L64_j8": {"T2*L^2/R^2": 0.5231, "T2*L^2/(R^2 ln(L/R))": 0.3773}, "2D_L128_j2": {"T2*L^2/R^2": 1.5549, "T2*L^2/(R^2 ln(L/R))": 0.4486}, "2D_L128_j4": {"T2*L^2/R^2": 1.2111, "T2*L^2/(R^2 ln(L/R))": 0.4368}, "2D_L128_j8": {"T2*L^2/R^2": 0.8566, "T2*L^2/(R^2 ln(L/R))": 0.412}, "2D_L256_j2": {"T2*L^2/R^2": 1.9172, "T2*L^2/(R^2 ln(L/R))": 0.461}, "2D_L256_j4": {"T2*L^2/R^2": 1.5777, "T2*L^2/(R^2 ln(L/R))": 0.4552}, "2D_L256_j8": {"T2*L^2/R^2": 1.2148, "T2*L^2/(R^2 ln(L/R))": 0.4381}, "2D_L512_j2": {"T2*L^2/R^2": 2.2807, "T2*L^2/(R^2 ln(L/R))": 0.4701}, "2D_L512_j4": {"T2*L^2/R^2": 1.9482, "T2*L^2/(R^2 ln(L/R))": 0.4684}, "2D_L512_j8": {"T2*L^2/R^2": 1.5834, "T2*L^2/(R^2 ln(L/R))": 0.4569}, "3D_L32_j2": {"T2*L^3/(|r||r'|)": 0.7596, "(K_br-l0(l+l'))*L^2": -0.0673, "(K_br-l0(l+l'-|r||r'|/L^3))*L^2": -0.0059, "(K_br-l0(l+l'))/(l0|r||r'|/L^3)": -1.0957}, "3D_L32_j4": {"T2*L^3/(|r||r'|)": 0.6439, "(K_br-l0(l+l'))*L^2": -0.1764, "(K_br-l0(l+l'-|r||r'|/L^3))*L^2": 0.0693, "(K_br-l0(l+l'))/(l0|r||r'|/L^3)": -0.7179}, "3D_L64_j2": {"T2*L^3/(|r||r'|)": 0.8363, "(K_br-l0(l+l'))*L^2": -0.0472, "(K_br-l0(l+l'-|r||r'|/L^3))*L^2": -0.0161, "(K_br-l0(l+l'))/(l0|r||r'|/L^3)": -1.5153}, "3D_L64_j4": {"T2*L^3/(|r||r'|)": 0.8045, "(K_br-l0(l+l'))*L^2": -0.1206, "(K_br-l0(l+l'-|r||r'|/L^3))*L^2": 0.004, "(K_br-l0(l+l'))/(l0|r||r'|/L^3)": -0.9681}, "3D_L64_j8": {"T2*L^3/(|r||r'|)": 0.6558, "(K_br-l0(l+l'))*L^2": -0.3448, "(K_br-l0(l+l'-|r||r'|/L^3))*L^2": 0.1536, "(K_br-l0(l+l'))/(l0|r||r'|/L^3)": -0.6918}, "3D_L128_j2": {"T2*L^3/(|r||r'|)": 0.8751, "(K_br-l0(l+l'))*L^2": -0.035, "(K_br-l0(l+l'-|r||r'|/L^3))*L^2": -0.0193, "(K_br-l0(l+l'))/(l0|r||r'|/L^3)": -2.2296}, "3D_L128_j4": {"T2*L^3/(|r||r'|)": 0.8886, "(K_br-l0(l+l'))*L^2": -0.0768, "(K_br-l0(l+l'-|r||r'|/L^3))*L^2": -0.014, "(K_br-l0(l+l'))/(l0|r||r'|/L^3)": -1.2238}, "3D_L128_j8": {"T2*L^3/(|r||r'|)": 0.8207, "(K_br-l0(l+l'))*L^2": -0.2262, "(K_br-l0(l+l'-|r||r'|/L^3))*L^2": 0.0247, "(K_br-l0(l+l'))/(l0|r||r'|/L^3)": -0.9015}} (R) 1D L=32: full contract vs reduction (3.1), max |diff|: (a) 8.88e-15, full grip 3.55e-15 (R) 2D L=8: full contract vs reduction (3.1), max |diff|: (a) 1.24e-14, full grip 1.29e-14 (R) 3D L=6: full contract vs reduction (3.1), max |diff|: (a) 3.55e-14, full grip 1.64e-14 (S) asymptotics of ell: {"2D_L64_ell0_minus_lnL_over_2pi": 0.04875850142855509, "2D_L128_ell0_minus_lnL_over_2pi": 0.048763848880206684, "2D_L256_ell0_minus_lnL_over_2pi": 0.04876518701309496, "2D_L512_ell0_minus_lnL_over_2pi": 0.048765521625585895, "2D_L512_ell(j)_minus_(3.10)_form": {"2": 0.00428, "4": 0.00099, "8": 0.00021, "16": 5e-05, "32": 1e-05, "64": 3e-05}, "3D_L32_ell0": 0.2456765511865084, "3D_L32_ell0_plus_xi3_over_L": 0.2527323299766616, "3D_L64_ell0": 0.24920328389380492, "3D_L64_ell0_plus_xi3_over_L": 0.2527311732888815, "3D_L96_ell0": 0.25037913173616777, "3D_L96_ell0_plus_xi3_over_L": 0.2527310579995522, "3D_L96_rel_dev_of_ell(j)_from_(3.11)_form": {"2": 0.07793, "4": 0.01983, "8": 0.00413, "16": 0.0014, "24": 0.00353}}