OUTPUT of run 4 of at most 100:
```
L0H3 VALUE/OUTPUT SPECTRA: possible alphabet-size evidence, not character labels
V [2.102 1.948 1.903 1.866 1.843 1.819 1.769 1.755 1.674 1.651 1.629 1.621 1.589 1.553 1.52  1.465 1.417 1.303 1.16  1.101 0.945 0.93  0.848 0.818 0.79  0.779 0.745 0.739 0.73
 0.701 0.688 0.658 0.642 0.622 0.618 0.605 0.575 0.565 0.543 0.522 0.515 0.491 0.481 0.466 0.446 0.43  0.41  0.4   0.378 0.366 0.359 0.349 0.345 0.342 0.336 0.329 0.318 0.313
 0.313 0.298 0.287 0.279 0.271 0.262]
O [2.133 2.11  2.076 1.975 1.963 1.937 1.913 1.891 1.878 1.845 1.823 1.813 1.78  1.737 1.713 1.678 1.632 1.457 1.395 1.326 1.286 1.272 1.214 1.201 1.19  1.131 1.101 1.078 1.065
 1.011 0.994 0.956 0.935 0.916 0.864 0.817 0.756 0.74  0.713 0.688 0.634 0.562 0.535 0.469 0.423 0.373 0.357 0.349 0.321 0.297 0.28  0.267 0.259 0.249 0.235 0.228 0.217 0.216
 0.198 0.187 0.184 0.172 0.145 0.127]
V times ln1 gain [0.57  0.513 0.504 0.472 0.47  0.451 0.44  0.434 0.425 0.412 0.39  0.383 0.38  0.367 0.36  0.344 0.339 0.337 0.324 0.298 0.286 0.276 0.273 0.266 0.255 0.249 0.245 0.241 0.237
 0.232 0.225 0.223 0.22  0.21  0.206 0.204 0.197 0.194 0.183 0.18  0.173 0.169 0.16  0.151 0.15  0.138 0.134 0.132 0.124 0.121 0.116 0.11  0.108 0.107 0.103 0.101 0.097 0.093
 0.09  0.087 0.085 0.081 0.078 0.072]
OV [1.127 0.955 0.95  0.89  0.864 0.854 0.844 0.78  0.759 0.723 0.709 0.674 0.67  0.652 0.634 0.617 0.565 0.528 0.438 0.382 0.35  0.317 0.297 0.295 0.282 0.276 0.265 0.246 0.24
 0.233 0.225 0.213 0.209 0.197 0.189 0.172 0.159 0.149 0.137 0.133 0.111 0.098 0.083 0.07  0.061 0.052 0.047 0.046 0.039 0.034 0.032 0.031 0.027 0.026 0.025 0.023 0.022 0.021
 0.021 0.018 0.018 0.015 0.013 0.011]

EARLY OV DOMINANT DIRECTIONS
H0 component 0 s=0.958 output [(336, 0.194), (96, 0.158), (291, -0.15), (327, 0.149), (203, -0.14), (202, -0.128), (330, 0.12), (68, -0.117)] input [(373, 0.174), (225, -0.164), (134, -0.158), (158, -0.155), (7, 0.152), (51, 0.148), (96, -0.142), (173, -0.132)]
H0 component 1 s=0.898 output [(39, -0.262), (6, -0.192), (282, 0.186), (156, 0.148), (163, 0.136), (152, 0.133), (342, 0.128), (219, -0.127)] input [(226, -0.165), (301, 0.154), (21, -0.146), (358, -0.145), (220, -0.13), (325, -0.129), (348, -0.127), (61, 0.126)]
H1 component 0 s=3.380 output [(39, 0.692), (58, -0.51), (99, 0.358), (21, -0.212), (184, 0.201), (153, -0.054), (336, -0.038), (63, 0.037)] input [(184, 0.347), (180, 0.315), (99, 0.271), (39, 0.267), (56, -0.254), (317, -0.239), (69, 0.235), (256, -0.214)]
H1 component 1 s=2.023 output [(21, 0.961), (39, 0.158), (58, -0.129), (184, 0.072), (306, -0.032), (173, -0.029), (225, -0.028), (232, -0.026)] input [(211, 0.341), (223, -0.262), (228, -0.244), (65, 0.232), (173, -0.229), (124, -0.213), (60, -0.212), (26, 0.189)]
H2 component 0 s=2.643 output [(39, -0.659), (58, 0.494), (21, 0.373), (99, -0.355), (184, -0.162), (153, 0.045), (383, -0.035), (165, -0.029)] input [(184, -0.365), (180, -0.304), (99, -0.298), (317, 0.248), (56, 0.234), (39, -0.232), (69, -0.208), (301, -0.195)]
H2 component 1 s=1.363 output [(21, 0.91), (39, 0.221), (99, 0.207), (58, -0.201), (184, 0.053), (252, -0.03), (351, -0.03), (153, -0.029)] input [(211, 0.3), (173, -0.273), (223, -0.256), (162, 0.227), (256, -0.225), (65, 0.222), (89, -0.205), (228, -0.196)]
H3 component 0 s=1.127 output [(92, 0.178), (86, -0.169), (188, 0.163), (18, -0.16), (131, -0.158), (303, -0.156), (215, -0.148), (173, -0.139)] input [(223, 0.227), (26, 0.198), (200, 0.172), (48, 0.168), (359, -0.144), (124, -0.141), (178, 0.137), (354, -0.133)]
H3 component 1 s=0.955 output [(65, -0.191), (125, -0.18), (320, 0.174), (202, 0.168), (86, 0.158), (287, 0.152), (20, -0.142), (350, -0.136)] input [(200, 0.228), (124, 0.181), (53, -0.178), (329, 0.169), (74, -0.167), (105, -0.159), (154, -0.15), (363, 0.15)]
H4 component 0 s=1.454 output [(39, -0.696), (58, 0.511), (99, -0.32), (184, -0.227), (21, -0.182), (153, 0.057), (336, 0.042), (350, 0.039)] input [(184, -0.414), (180, -0.29), (256, 0.279), (56, 0.243), (100, 0.236), (69, -0.226), (317, 0.207), (162, -0.199)]
H4 component 1 s=0.724 output [(21, 0.941), (99, -0.241), (39, -0.097), (58, 0.092), (184, 0.042), (148, -0.033), (52, -0.032), (381, 0.031)] input [(211, 0.354), (228, -0.271), (65, 0.22), (124, -0.217), (26, 0.216), (319, 0.214), (223, -0.201), (59, 0.188)]
H5 component 0 s=16.282 output [(21, -0.864), (99, -0.358), (58, 0.237), (39, -0.232), (184, 0.024), (153, 0.019), (303, 0.019), (6, 0.017)] input [(162, -0.329), (211, -0.307), (223, 0.277), (65, -0.236), (354, 0.201), (173, 0.2), (132, -0.196), (300, -0.192)]
H5 component 1 s=8.786 output [(39, -0.608), (58, 0.486), (21, 0.469), (99, -0.404), (180, -0.035), (165, -0.026), (153, 0.021), (86, -0.015)] input [(99, -0.371), (180, -0.317), (184, -0.311), (162, -0.225), (100, 0.207), (240, -0.205), (317, 0.205), (39, -0.203)]

LATER AFFINE KEY DIRECTIONS VS L0 OV OUTPUT SUBSPACES
L1H0: fractions [0.001 0.82  0.833 0.    0.783 0.847] largest coordinates [(21, 3.627), (39, -0.474), (58, 0.358), (329, -0.211), (304, -0.198)]
L1H1: fractions [0.    0.822 0.836 0.006 0.767 0.848] largest coordinates [(21, 3.352), (58, 0.506), (39, -0.427), (57, 0.256), (187, 0.193)]
L1H2: fractions [0.    0.817 0.831 0.    0.766 0.849] largest coordinates [(21, 2.769), (58, 0.4), (39, -0.389), (215, 0.212), (369, -0.195)]
L1H3: fractions [0.    0.827 0.833 0.009 0.793 0.848] largest coordinates [(21, 3.079), (58, 0.459), (39, -0.423), (170, -0.29), (242, 0.209)]
L1H4: fractions [0.001 0.788 0.783 0.005 0.764 0.792] largest coordinates [(21, 2.008), (58, 0.505), (39, -0.333), (150, 0.179), (144, -0.164)]
L1H5: fractions [0.    0.837 0.839 0.001 0.796 0.849] largest coordinates [(21, 3.563), (39, -0.485), (58, 0.399), (351, -0.267), (210, -0.249)]
L2H0: fractions [0.    0.811 0.818 0.003 0.777 0.828] largest coordinates [(21, 1.815), (39, -0.266), (58, 0.248), (294, -0.155), (351, 0.141)]
L2H1: fractions [0.    0.815 0.799 0.    0.78  0.809] largest coordinates [(21, 1.682), (99, -0.208), (58, 0.201), (39, -0.199), (255, -0.119)]
L2H2: fractions [0.001 0.789 0.768 0.003 0.778 0.772] largest coordinates [(21, 1.411), (99, -0.238), (58, 0.156), (39, -0.151), (306, 0.099)]
L2H3: fractions [0.003 0.62  0.624 0.002 0.589 0.611] largest coordinates [(21, 0.803), (58, 0.158), (39, -0.133), (99, -0.117), (363, 0.096)]
L2H4: fractions [0.001 0.783 0.805 0.    0.745 0.826] largest coordinates [(21, 2.069), (58, 0.32), (39, -0.29), (361, -0.13), (2, 0.126)]
L2H5: fractions [0.001 0.83  0.836 0.002 0.786 0.847] largest coordinates [(21, 1.859), (58, 0.204), (39, -0.17), (40, 0.102), (214, 0.1)]
L3H0: fractions [0.004 0.708 0.692 0.014 0.687 0.685] largest coordinates [(21, 0.408), (39, -0.069), (99, -0.067), (307, 0.041), (58, 0.04)]
L3H1: fractions [0.041 0.508 0.493 0.007 0.482 0.474] largest coordinates [(21, 0.181), (39, -0.058), (184, -0.048), (99, -0.046), (37, 0.03)]
L3H2: fractions [0.002 0.649 0.623 0.008 0.639 0.615] largest coordinates [(21, 0.382), (99, -0.095), (39, -0.065), (25, -0.044), (136, -0.037)]
L3H3: fractions [0.013 0.009 0.01  0.005 0.009 0.008] largest coordinates [(193, -0.036), (157, 0.031), (198, -0.029), (339, -0.029), (129, -0.029)]
L3H4: fractions [0.112 0.037 0.043 0.001 0.032 0.037] largest coordinates [(163, -0.031), (21, 0.028), (120, 0.023), (355, -0.022), (269, -0.021)]
L3H5: fractions [0.001 0.737 0.734 0.006 0.691 0.721] largest coordinates [(21, 0.416), (39, -0.064), (184, -0.059), (22, 0.046), (43, 0.043)]

MLP0 ROW GEOMETRY
current weight projection singular values [11.423  8.653  7.882  7.526  7.341  7.074  6.711  6.614  6.451  5.991  5.713  5.275  5.123  4.988  4.568  4.471  4.337  4.154  4.05   3.687  2.842  2.48   1.813  1.73   1.422
  1.334  1.069]
row norm percentiles [0.058 0.102 0.122 0.185 0.905 1.334 1.93  2.293]
previous-head path projection singular values [9.585 6.439 6.141 5.846 5.572 5.342 5.241 5.049 4.705 4.621 4.247 3.991 3.704 3.634 3.478 2.674 2.396 1.701 1.277 0.899 0.859 0.484 0.373 0.35  0.297 0.27  0.252]
row norm percentiles [0.035 0.052 0.063 0.093 0.649 1.022 1.463 2.334]
current/previous weight cross spectrum [62.36  22.22  17.069 16.491 14.485 12.829 11.603  9.646  8.392  6.824  6.069  5.712  4.763  4.273  3.802  3.06   2.612  2.219  2.058  1.591  0.764  0.526  0.267  0.212  0.148
  0.055  0.002]
cross symmetric eigenvalues [-12.298 -11.004  -8.306  -7.578  -6.48   -4.526  -2.956  -2.131  -1.505  -0.943  -0.71   -0.46   -0.065   0.379   0.46    1.018   1.305   1.424   2.432   3.238   4.683   5.521
   6.414   9.651  10.927  15.3    52.67 ]
cross trace/F 0.7401727646232719

```