# band_scan.py results (numerical exploration, not proofs), 2026-10-22 UTC
## far_theta0.7
check: delta_sqrt2 -> 0.8577638849604883 target 0.8577638849607068
far theta 0.70 rho2 0.050: sup 0.84383 (sqrt(2/e)-0.01393)  w=[0.9389 0.0111 0.0018 0.0286 0.0167 0.003 ] c=[ 1.3594  1.3594 -1.3536 -1.3536  0.4783  0.4783] w0=0.0000
far theta 0.70 rho2 0.100: sup 0.83169 (sqrt(2/e)-0.02608)  w=[0.8791 0.0209 0.0035 0.0572 0.0334 0.0059] c=[ 1.3066  1.3066 -1.288  -1.288   0.4819  0.4819] w0=0.0000
far theta 0.70 rho2 0.200: sup 0.81533 (sqrt(2/e)-0.04243)  w=[0.092  0.0304 0.7924 0.0076 0.0591 0.0185] c=[ 1.0075  1.0075 -1.0727 -1.0727  0.7    -0.7   ] w0=0.0000
far theta 0.70 rho2 0.300: sup 0.81117 (sqrt(2/e)-0.04659)  w=[0. 0. 0. 0. 0. 1.] c=[ 0.7     2.5004 -1.0667 -2.8469  0.6275 -0.6325] w0=0.0000
far theta 0.70 rho2 0.500: sup 0.81117 (sqrt(2/e)-0.04659)  w=[0. 0. 0. 0. 0. 1.] c=[ 0.7     2.5004 -1.0667 -2.8469  0.6275 -0.6325] w0=0.0000
## far_theta08
check: delta_sqrt2 -> 0.8577638849604883 target 0.8577638849607068
far theta 0.80 rho2 0.050: sup 0.84614 (sqrt(2/e)-0.01162)  w=[0.00e+00 9.50e-01 1.99e-02 3.00e-04 8.30e-03 2.15e-02] c=[ 2.6006  1.3753 -1.2999 -1.2999 -0.8     0.8   ] w0=0.0000
far theta 0.80 rho2 0.100: sup 0.83641 (sqrt(2/e)-0.02135)  w=[0.00e+00 9.00e-01 3.98e-02 6.00e-04 1.67e-02 4.30e-02] c=[ 2.6006  1.3331 -1.2032 -1.2032 -0.8     0.8   ] w0=0.0000
far theta 0.80 rho2 0.200: sup 0.82204 (sqrt(2/e)-0.03572)  w=[0.     0.8    0.0796 0.0011 0.0333 0.0859] c=[ 2.6006  1.2389 -1.0564 -1.0564 -0.8     0.8   ] w0=0.0000
far theta 0.80 rho2 0.300: sup 0.81353 (sqrt(2/e)-0.04423)  w=[0.7    0.     0.0728 0.1185 0.     0.1088] c=[ 1.1097  2.746  -0.9561 -0.9561  0.6471  0.8   ] w0=0.0000
far theta 0.80 rho2 0.400: sup 0.80819 (sqrt(2/e)-0.04958)  w=[0.6    0.     0.153  0.0567 0.0636 0.1267] c=[ 1.0353  2.746  -0.8    -0.8     0.8     0.8   ] w0=0.0000
## far_theta1.0
check: delta_sqrt2 -> 0.8577638849604883 target 0.8577638849607068
far theta 1.00 rho2 0.050: sup 0.85391 (sqrt(2/e)-0.00385)  w=[0.000e+00 0.000e+00 6.785e-01 2.715e-01 6.000e-04 4.940e-02] c=[ 2.5123  1.3836 -1.4279 -1.4279  1.     -1.    ] w0=0.0000
far theta 1.00 rho2 0.100: sup 0.84983 (sqrt(2/e)-0.00793)  w=[0.     0.     0.4667 0.4333 0.0022 0.0978] c=[ 2.5123  1.3836 -1.4402 -1.4402  1.     -1.    ] w0=0.0000
far theta 1.00 rho2 0.200: sup 0.84142 (sqrt(2/e)-0.01634)  w=[0.     0.     0.2498 0.5502 0.0069 0.1931] c=[ 2.5123  1.3836 -1.4635 -1.4635  1.     -1.    ] w0=0.0000
far theta 1.00 rho2 0.300: sup 0.83335 (sqrt(2/e)-0.02442)  w=[0.     0.     0.     0.7    0.0257 0.2743] c=[ 1.4367  2.2654 -2.3212 -1.4532  1.     -1.    ] w0=0.0000
far theta 1.00 rho2 0.500: sup 0.82348 (sqrt(2/e)-0.03428)  w=[0.0592 0.     0.     0.5    0.048  0.3928] c=[ 1.      2.2654 -2.3212 -1.3075  0.9379 -1.    ] w0=0.0000
## band_theta0.7
check: delta_sqrt2 -> 0.8577638849604883 target 0.8577638849607068
band theta 0.70 rho2 0.010 eta 0.0018: sup excess -0.00171  lamS 0.5472  w=[0.99 0.   0.   0.01] c=[ 1.345   2.4714 -0.4339 -1.2345] w0=0.0000 E|Z|=0.85425
band theta 0.70 rho2 0.030 eta 0.0018: sup excess -0.00527  lamS 0.5472  w=[0.97 0.   0.03 0.  ] c=[ 1.3314  2.686  -1.2542  0.0496] w0=0.0000 E|Z|=0.85069
band theta 0.70 rho2 0.100 eta 0.0018: sup excess -0.01881  lamS 0.5625  w=[0.9 0.  0.  0.1] c=[ 1.2649  2.8198 -1.3057 -1.2649] w0=0.0000 E|Z|=0.83715
band theta 0.70 rho2 0.300 eta 0.0018: sup excess -0.04225  lamS 0.3602  w=[0.7 0.  0.  0.3] c=[ 1.3941  2.7115 -2.0979  0.6449] w0=0.0000 E|Z|=0.81371
## band_theta08
check: delta_sqrt2 -> 0.8577638849604883 target 0.8577638849607068
band theta 0.80 rho2 0.010 eta 0.0018: sup excess -0.00171  lamS 0.5472  w=[0.   0.99 0.   0.01] c=[ 1.0941  1.345  -1.8352 -1.2345] w0=0.0000 E|Z|=0.85425
band theta 0.80 rho2 0.020 eta 0.0018: sup excess -0.00347  lamS 0.5472  w=[0.   0.98 0.   0.02] c=[ 1.0941  1.3382 -1.8352 -1.2446] w0=0.0000 E|Z|=0.85249
band theta 0.80 rho2 0.050 eta 0.0018: sup excess -0.00899  lamS 0.5472  w=[0.   0.95 0.   0.05] c=[ 2.4635  1.3176 -0.343  -1.2724] w0=0.0000 E|Z|=0.84698
band theta 0.80 rho2 0.100 eta 0.0018: sup excess -0.01881  lamS 0.5625  w=[0.  0.9 0.  0.1] c=[ 1.2979  1.2649 -1.2664 -1.2649] w0=0.0000 E|Z|=0.83715
band theta 0.80 rho2 0.200 eta 0.0018: sup excess -0.03288  lamS 0.5472  w=[0.8    0.     0.1343 0.0657] c=[ 1.2091  2.8286 -1.0669  0.8   ] w0=0.0000 E|Z|=0.82309
band theta 0.80 rho2 0.300 eta 0.0018: sup excess -0.03620  lamS 1.0355  w=[0.7 0.  0.3 0. ] c=[ 0.8222  1.4035  0.8    -1.7809] w0=0.0000 E|Z|=0.81976
## band_theta1.0
check: delta_sqrt2 -> 0.8577638849604883 target 0.8577638849607068
band theta 1.00 rho2 0.010 eta 0.0018: sup excess -0.00021  lamS 0.4556  w=[0.   0.99 0.01 0.  ] c=[ 2.8129  1.4742  1.     -0.6084] w0=0.0000 E|Z|=0.85575
band theta 1.00 rho2 0.030 eta 0.0018: sup excess -0.00093  lamS 0.4556  w=[0.   0.97 0.03 0.  ] c=[ 2.8129  1.4592  1.     -0.6084] w0=0.0000 E|Z|=0.85503
band theta 1.00 rho2 0.100 eta 0.0018: sup excess -0.00591  lamS 0.4308  w=[0.9 0.  0.  0.1] c=[ 1.4454  2.4782 -1.4925  1.    ] w0=0.0000 E|Z|=0.85006
band theta 1.00 rho2 0.300 eta 0.0018: sup excess -0.02367  lamS 0.6027  w=[0.  0.7 0.3 0. ] c=[ 2.1218  1.5207  1.     -1.9679] w0=0.0000 E|Z|=0.83229
