OUTPUT of run 7 of at most 100:
```
CENTERED WEIGHT DIAGNOSTICS
QKnorm; QK effective rank; trace/F; key-affine norm; fraction of key-affine energy at coordinate 21
L0H0 [ 0.293  1.893 -0.357  0.043  0.019]
L0H1 [ 0.159  1.248 -0.619  0.013  0.   ]
L0H2 [ 0.107  1.209 -0.813  0.007  0.   ]
L0H3 [ 0.698 17.073  1.923  0.043  0.016]
L0H4 [ 0.088  1.514 -0.519  0.017  0.009]
L0H5 [ 0.034  1.229 -0.253  0.005  0.003]
L1H0 [ 1.978  5.901 -0.884  3.974  0.831]
L1H1 [ 1.843  5.076 -0.845  3.688  0.824]
L1H2 [ 1.781  4.525 -1.06   3.051  0.822]
L1H3 [ 1.787  4.33  -0.846  3.39   0.824]
L1H4 [ 1.629  4.856 -1.234  2.329  0.742]
L1H5 [ 1.863  5.366 -0.875  3.895  0.835]
L2H0 [ 1.631 16.641 -0.953  2.02   0.804]
L2H1 [ 2.154 31.479 -0.1    1.88   0.799]
L2H2 [ 1.72  31.296 -0.754  1.608  0.767]
L2H3 [ 1.623 31.026 -0.367  1.06   0.575]
L2H4 [ 2.215 22.89  -0.442  2.305  0.802]
L2H5 [ 2.264 30.297 -0.118  2.023  0.842]
L3H0 [ 2.029 44.28   1.073  0.5    0.663]
L3H1 [ 1.216 34.005  0.355  0.28   0.416]
L3H2 [ 1.437 40.138  0.243  0.495  0.595]
L3H3 [ 1.815 53.475  3.212  0.22   0.003]
L3H4 [ 0.623 19.228  0.003  0.144  0.037]
L3H5 [ 1.665 41.691  0.863  0.493  0.71 ]

KEY-SIDE MATCHING, WITH BROKEN-OV-PAIRING CONTROLS
subspace rank 16
L1H1: actual=0.690 null_mean=0.083 null_sd=0.240 null_max=0.828
L1H2: actual=0.474 null_mean=0.045 null_sd=0.239 null_max=0.744
L1H5: actual=0.552 null_mean=0.041 null_sd=0.252 null_max=0.774
L2H4: actual=0.796 null_mean=0.066 null_sd=0.233 null_max=0.796
L3H0: actual=-0.734 null_mean=-0.065 null_sd=0.227 null_max=0.559
L3H3: actual=2.724 null_mean=0.042 null_sd=0.247 null_max=0.684
L3H4: actual=0.652 null_mean=-0.006 null_sd=0.247 null_max=0.687
subspace rank 20
L1H1: actual=0.632 null_mean=0.087 null_sd=0.217 null_max=0.701
L1H2: actual=0.482 null_mean=0.037 null_sd=0.207 null_max=0.575
L1H5: actual=0.518 null_mean=0.036 null_sd=0.228 null_max=0.659
L2H4: actual=0.708 null_mean=0.058 null_sd=0.218 null_max=0.776
L3H0: actual=-0.629 null_mean=-0.062 null_sd=0.202 null_max=0.493
L3H3: actual=2.858 null_mean=0.049 null_sd=0.226 null_max=0.655
L3H4: actual=0.682 null_mean=-0.001 null_sd=0.224 null_max=0.618
subspace rank 24
L1H1: actual=0.580 null_mean=0.070 null_sd=0.204 null_max=0.574
L1H2: actual=0.508 null_mean=0.026 null_sd=0.184 null_max=0.443
L1H5: actual=0.480 null_mean=0.033 null_sd=0.211 null_max=0.619
L2H4: actual=0.727 null_mean=0.044 null_sd=0.202 null_max=0.793
L3H0: actual=-0.614 null_mean=-0.044 null_sd=0.184 null_max=0.476
L3H3: actual=2.716 null_mean=0.034 null_sd=0.212 null_max=0.586
L3H4: actual=0.593 null_mean=0.001 null_sd=0.205 null_max=0.558
subspace rank 28
L1H1: actual=0.573 null_mean=0.069 null_sd=0.192 null_max=0.533
L1H2: actual=0.494 null_mean=0.023 null_sd=0.175 null_max=0.427
L1H5: actual=0.483 null_mean=0.034 null_sd=0.198 null_max=0.602
L2H4: actual=0.645 null_mean=0.028 null_sd=0.188 null_max=0.659
L3H0: actual=-0.585 null_mean=-0.036 null_sd=0.175 null_max=0.457
L3H3: actual=2.614 null_mean=0.026 null_sd=0.203 null_max=0.600
L3H4: actual=0.523 null_mean=0.004 null_sd=0.191 null_max=0.487
subspace rank 32
L1H1: actual=0.567 null_mean=0.065 null_sd=0.186 null_max=0.506
L1H2: actual=0.478 null_mean=0.025 null_sd=0.168 null_max=0.401
L1H5: actual=0.489 null_mean=0.039 null_sd=0.186 null_max=0.573
L2H4: actual=0.598 null_mean=0.032 null_sd=0.177 null_max=0.655
L3H0: actual=-0.593 null_mean=-0.032 null_sd=0.167 null_max=0.473
L3H3: actual=2.505 null_mean=0.027 null_sd=0.190 null_max=0.554
L3H4: actual=0.477 null_mean=0.004 null_sd=0.181 null_max=0.486

L0H0 RELATIVE ROTATION CHECK: ROBUSTNESS TO SUBSPACE SIZE
rank 24 best [(4, 0.24811147243940024), (3, 0.21456492278914205), (5, 0.13972628524098518), (-3, 0.08686549543323072), (-4, 0.05001577182505205)]
rank 32 best [(4, 0.21871870766887486), (3, 0.16649449461447283), (5, 0.13166180385313234), (-3, 0.07522594557246681), (-4, 0.05806725638638227)]
rank 40 best [(4, 0.15680824363317394), (5, 0.11052788607755092), (3, 0.10991298663568431), (-4, 0.060306698329549525), (-3, 0.05568532840411643)]
rank 48 best [(4, 0.14490451598858572), (3, 0.12561806339108184), (5, 0.10801204262920121), (-4, 0.06819183410170707), (-5, 0.052344841947909476)]
rank 56 best [(4, 0.13409521327824356), (5, 0.12145249348505678), (3, 0.10839131918587229), (-4, 0.051381216474243305), (6, 0.05000059909522994)]

```