OUTPUT of run 6 of at most 100:
```
MATCHING-PATH DIAGNOSTICS
Each pair is trace/F, symmetric_fraction.
00=direct/direct; 01=direct/earlier-OV; 10=earlier-OV/direct; 11=earlier-OV/both.
L1H0 full [[-0.883  0.722]
 [ 0.102  0.712]
 [-0.071  0.706]
 [-0.286  0.717]] V-subspace [[-2.198  0.855]
 [ 0.314  0.743]
 [-0.161  0.697]
 [-0.278  0.717]]
L1H1 full [[-0.845  0.713]
 [ 0.216  0.713]
 [ 0.245  0.713]
 [-1.006  0.753]] V-subspace [[-1.965  0.822]
 [ 0.577  0.747]
 [ 0.514  0.737]
 [-1.01   0.754]]
L1H2 full [[-1.059  0.72 ]
 [ 0.167  0.713]
 [-0.177  0.708]
 [-1.974  0.859]] V-subspace [[-1.49   0.782]
 [ 0.507  0.762]
 [-0.417  0.714]
 [-1.986  0.86 ]]
L1H3 full [[-0.844  0.709]
 [ 0.076  0.712]
 [ 0.054  0.701]
 [-0.894  0.735]] V-subspace [[-1.826  0.806]
 [ 0.209  0.753]
 [ 0.141  0.683]
 [-0.892  0.736]]
L1H4 full [[-1.234  0.723]
 [ 0.015  0.708]
 [-0.798  0.727]
 [-2.572  0.884]] V-subspace [[-1.662  0.788]
 [ 0.071  0.712]
 [-1.945  0.822]
 [-2.58   0.886]]
L1H5 full [[-0.874  0.713]
 [ 0.198  0.717]
 [ 0.208  0.709]
 [-0.381  0.704]] V-subspace [[-2.219  0.845]
 [ 0.477  0.774]
 [ 0.436  0.724]
 [-0.372  0.704]]
L2H0 full [[-0.954  0.693]
 [ 0.079  0.708]
 [-0.153  0.712]
 [-2.011  0.796]] V-subspace [[-1.039  0.722]
 [ 0.25   0.721]
 [-0.54   0.762]
 [-2.024  0.802]]
L2H1 full [[-0.1    0.7  ]
 [ 0.009  0.71 ]
 [ 0.081  0.711]
 [-1.008  0.726]] V-subspace [[-0.588  0.721]
 [-0.008  0.751]
 [ 0.237  0.752]
 [-1.025  0.727]]
L2H2 full [[-0.754  0.706]
 [ 0.099  0.707]
 [-0.182  0.709]
 [-1.854  0.795]] V-subspace [[-0.818  0.727]
 [ 0.388  0.703]
 [-0.717  0.73 ]
 [-1.865  0.8  ]]
L2H3 full [[-0.367  0.704]
 [ 0.082  0.709]
 [ 0.101  0.71 ]
 [-1.124  0.73 ]] V-subspace [[-0.428  0.697]
 [ 0.367  0.746]
 [ 0.358  0.759]
 [-1.173  0.731]]
L2H4 full [[-0.443  0.696]
 [ 0.159  0.71 ]
 [-0.015  0.707]
 [-1.687  0.766]] V-subspace [[-0.336  0.716]
 [ 0.72   0.766]
 [-0.027  0.69 ]
 [-1.723  0.77 ]]
L2H5 full [[-0.118  0.699]
 [ 0.01   0.708]
 [ 0.216  0.713]
 [-0.9    0.765]] V-subspace [[-0.835  0.734]
 [ 0.002  0.724]
 [ 0.591  0.754]
 [-0.935  0.767]]
L3H0 full [[ 1.073  0.709]
 [-0.177  0.707]
 [ 0.119  0.711]
 [-0.504  0.746]] V-subspace [[ 0.245  0.67 ]
 [-0.612  0.704]
 [ 0.567  0.756]
 [-0.587  0.751]]
L3H1 full [[ 0.353  0.706]
 [-0.033  0.707]
 [ 0.074  0.711]
 [ 0.326  0.707]] V-subspace [[ 0.214  0.719]
 [-0.133  0.719]
 [ 0.258  0.744]
 [ 0.322  0.706]]
L3H2 full [[ 0.242  0.703]
 [ 0.033  0.709]
 [-0.027  0.707]
 [-0.452  0.752]] V-subspace [[-0.019  0.684]
 [ 0.117  0.735]
 [-0.022  0.704]
 [-0.489  0.755]]
L3H3 full [[ 3.2    0.778]
 [ 0.922  0.73 ]
 [-0.376  0.711]
 [ 2.364  0.821]] V-subspace [[ 0.875  0.8  ]
 [ 2.718  0.877]
 [-1.432  0.77 ]
 [ 2.316  0.828]]
L3H4 full [[ 0.001  0.708]
 [ 0.124  0.708]
 [-0.046  0.71 ]
 [ 0.199  0.728]] V-subspace [[ 0.2    0.71 ]
 [ 0.574  0.715]
 [-0.054  0.757]
 [ 0.169  0.729]]
L3H5 full [[ 0.863  0.71 ]
 [-0.062  0.708]
 [ 0.228  0.709]
 [-0.333  0.736]] V-subspace [[ 0.121  0.686]
 [-0.173  0.716]
 [ 0.829  0.734]
 [-0.395  0.735]]

L0H3 PATH TO L3H3: POSITIVE/NEGATIVE SYMMETRIC ENERGY
direct positive squared-eigenvalue fraction 0.8311817865380196 top positive [0.229 0.229 0.233 0.24  0.241 0.244 0.253 0.257] most negative [-0.189 -0.165 -0.161 -0.147 -0.138 -0.134 -0.125 -0.121]
key via H3 positive squared-eigenvalue fraction 0.7259420110120174 top positive [0.061 0.065 0.072 0.074 0.081 0.085 0.097 0.109] most negative [-0.068 -0.056 -0.05  -0.045 -0.042 -0.042 -0.038 -0.036]
query via H3 positive squared-eigenvalue fraction 0.41474673409113433 top positive [0.043 0.046 0.047 0.05  0.054 0.058 0.063 0.067] most negative [-0.079 -0.076 -0.071 -0.063 -0.06  -0.059 -0.056 -0.052]
both via H3 positive squared-eigenvalue fraction 0.9652646152209285 top positive [0.012 0.015 0.019 0.021 0.025 0.026 0.033 0.043] most negative [-0.01  -0.007 -0.006 -0.003 -0.003 -0.001 -0.001 -0.001]

ICA OF FINAL MLP OUTPUT COLUMNS (weights only; no neural computation)
components 22 iterations 917 warnings 0
mixing norm, excess kurtosis: [[ 0.585 -0.438]
 [ 0.555 -0.582]
 [ 0.527  2.328]
 [ 0.492 -0.353]
 [ 0.491  1.23 ]
 [ 0.467  1.665]
 [ 0.466  1.051]
 [ 0.465  1.808]
 [ 0.462  1.407]
 [ 0.451  0.838]
 [ 0.44   0.871]
 [ 0.437  2.203]
 [ 0.412  1.79 ]
 [ 0.403  1.388]
 [ 0.398  1.148]
 [ 0.397  1.83 ]
 [ 0.395  0.928]
 [ 0.393  2.406]
 [ 0.342  0.895]
 [ 0.337  1.73 ]
 [ 0.332  3.369]
 [ 0.244  5.268]]
components 24 iterations 310 warnings 0
mixing norm, excess kurtosis: [[ 0.54  -0.489]
 [ 0.526 -0.574]
 [ 0.523  2.737]
 [ 0.483 -0.463]
 [ 0.478  1.504]
 [ 0.466  1.742]
 [ 0.464  1.691]
 [ 0.455  0.631]
 [ 0.447  1.569]
 [ 0.446  0.984]
 [ 0.444  0.408]
 [ 0.432  1.985]
 [ 0.426  1.134]
 [ 0.424  2.28 ]
 [ 0.39   1.494]
 [ 0.387  2.185]
 [ 0.381  2.436]
 [ 0.366  1.136]
 [ 0.366  1.477]
 [ 0.345  1.107]
 [ 0.344  1.424]
 [ 0.331  1.998]
 [ 0.328  2.904]
 [ 0.244 11.27 ]]
components 27 iterations 187 warnings 0
mixing norm, excess kurtosis: [[ 0.516 -0.558]
 [ 0.513 -0.524]
 [ 0.498 -0.448]
 [ 0.48   1.51 ]
 [ 0.456  1.724]
 [ 0.455  1.541]
 [ 0.433  1.545]
 [ 0.432  0.781]
 [ 0.423  2.317]
 [ 0.417  1.96 ]
 [ 0.414  1.531]
 [ 0.398  1.675]
 [ 0.397  0.635]
 [ 0.39   2.752]
 [ 0.388  2.418]
 [ 0.387  1.837]
 [ 0.382  0.954]
 [ 0.382  1.401]
 [ 0.38  15.42 ]
 [ 0.361  1.259]
 [ 0.356  4.616]
 [ 0.346  1.325]
 [ 0.344  1.498]
 [ 0.334  1.459]
 [ 0.317  2.706]
 [ 0.292  1.385]
 [ 0.236 12.664]]
components 30 iterations 1151 warnings 0
mixing norm, excess kurtosis: [[ 0.47   1.641]
 [ 0.453 -0.492]
 [ 0.452  1.487]
 [ 0.45   1.528]
 [ 0.447  1.167]
 [ 0.437  2.442]
 [ 0.412  1.03 ]
 [ 0.408  1.705]
 [ 0.408  1.568]
 [ 0.405  3.77 ]
 [ 0.403  0.834]
 [ 0.396  2.218]
 [ 0.392  0.966]
 [ 0.391  3.051]
 [ 0.383 -0.465]
 [ 0.382  1.463]
 [ 0.381  2.461]
 [ 0.38   1.318]
 [ 0.372  1.602]
 [ 0.356 19.442]
 [ 0.35   2.216]
 [ 0.345  1.398]
 [ 0.339  1.699]
 [ 0.335  1.48 ]
 [ 0.331  1.386]
 [ 0.327  1.258]
 [ 0.324  7.047]
 [ 0.312  1.476]
 [ 0.311 11.721]
 [ 0.238 12.48 ]]

CLOCK-REGISTER WRITE STRENGTHS
L0H0: row21 norm=0.047 row21 energy fraction=0.000 rows21,39,58,99 combined fraction=0.029
L0H1: row21 norm=2.072 row21 energy fraction=0.271 rows21,39,58,99 combined fraction=0.908
L0H2: row21 norm=1.585 row21 energy fraction=0.273 rows21,39,58,99 combined fraction=0.918
L0H3: row21 norm=0.055 row21 energy fraction=0.000 rows21,39,58,99 combined fraction=0.003
L0H4: row21 norm=0.732 row21 energy fraction=0.189 rows21,39,58,99 combined fraction=0.838
L0H5: row21 norm=14.657 row21 energy fraction=0.607 rows21,39,58,99 combined fraction=0.963
Exact LayerNorm gains at coordinate 21: {'ln1_w.0': 0.5348148345947266, 'ln2_w.0': 0.11408951133489609, 'ln1_w.1': 1.084619402885437, 'ln2_w.1': 0.0018652267754077911, 'ln1_w.2': 1.0927202701568604, 'ln2_w.2': 0.01202222891151905, 'ln1_w.3': 0.8020247220993042, 'ln2_w.3': 0.23280216753482819}

```