OUTPUT of run 6 of at most 100:
```
V effective head 1 singular values [0.48  0.455 0.448 0.429 0.421 0.41  0.403 0.385 0.379 0.373 0.37  0.36  0.353 0.341 0.33  0.327 0.322 0.313 0.309 0.303 0.295 0.287 0.281 0.278
 0.27  0.255 0.253 0.241 0.226 0.216 0.209 0.201 0.198 0.171 0.164 0.159 0.155 0.148 0.145 0.143 0.137 0.134 0.126 0.124 0.117]
V effective head 5 singular values [0.493 0.473 0.446 0.437 0.426 0.408 0.404 0.393 0.386 0.376 0.363 0.361 0.356 0.345 0.333 0.329 0.322 0.316 0.31  0.304 0.299 0.289 0.285 0.277
 0.274 0.267 0.252 0.245 0.241 0.235 0.233 0.221 0.216 0.212 0.208 0.203 0.199 0.194 0.188 0.179 0.169 0.164 0.157 0.143 0.138]

Common L0H1/L0H5 value-input subspaces:
12 [0.923 0.908 0.879 0.832 0.787 0.707 0.659 0.531 0.416 0.281 0.231 0.023]
20 [0.963 0.943 0.935 0.924 0.921 0.907 0.891 0.883 0.87  0.868 0.856 0.84  0.798 0.773 0.581 0.559 0.506 0.353 0.134 0.034]
24 [0.966 0.958 0.957 0.946 0.936 0.932 0.923 0.912 0.909 0.895 0.891 0.874 0.862 0.843 0.839 0.785 0.675 0.639 0.587 0.549 0.425 0.287 0.156 0.005]
28 [0.972 0.966 0.959 0.957 0.946 0.94  0.938 0.934 0.931 0.918 0.913 0.9   0.889 0.883 0.872 0.849 0.836 0.81  0.8   0.788 0.702 0.615 0.55  0.482
 0.427 0.356 0.193 0.048]
32 [0.977 0.969 0.961 0.958 0.951 0.946 0.945 0.943 0.939 0.931 0.925 0.917 0.912 0.905 0.885 0.875 0.872 0.858 0.839 0.82  0.787 0.727 0.708 0.666
 0.61  0.567 0.487 0.385 0.262 0.133 0.083 0.013]
40 [0.981 0.975 0.971 0.966 0.963 0.958 0.956 0.952 0.948 0.947 0.946 0.936 0.933 0.927 0.918 0.913 0.898 0.894 0.886 0.883 0.864 0.839 0.825 0.804
 0.792 0.756 0.74  0.694 0.671 0.633 0.548 0.531 0.502 0.471 0.344 0.304 0.232 0.088 0.057 0.017]
48 [0.984 0.98  0.974 0.973 0.97  0.967 0.964 0.962 0.956 0.955 0.949 0.946 0.942 0.939 0.929 0.927 0.925 0.911 0.899 0.896 0.885 0.866 0.866 0.854
 0.835 0.82  0.802 0.786 0.762 0.747 0.729 0.706 0.693 0.647 0.614 0.6   0.518 0.476 0.445 0.418 0.319 0.317 0.289 0.258 0.15  0.134 0.059 0.049]
64 [0.987 0.984 0.98  0.98  0.977 0.974 0.972 0.97  0.97  0.966 0.961 0.96  0.958 0.953 0.95  0.945 0.938 0.935 0.928 0.924 0.917 0.902 0.897 0.892
 0.881 0.879 0.856 0.853 0.833 0.828 0.812 0.795 0.785 0.781 0.743 0.727 0.71  0.69  0.657 0.65  0.632 0.609 0.571 0.564 0.555 0.504 0.478 0.461
 0.426 0.415 0.395 0.382 0.36  0.339 0.306 0.253 0.241 0.209 0.194 0.12  0.073 0.067 0.053 0.023]

Joint value-input eigenvalues [0.408 0.386 0.353 0.348 0.326 0.295 0.289 0.28  0.266 0.264 0.244 0.239 0.225 0.222 0.218 0.205 0.201 0.198 0.19  0.178 0.173 0.157 0.145 0.145
 0.131 0.126 0.125 0.112 0.107 0.095 0.089 0.083 0.082 0.076 0.075 0.067 0.066 0.064 0.059 0.056 0.053 0.051 0.05  0.049 0.041 0.037 0.033 0.032
 0.03  0.029]

Projected FC0 rank 20 active 531 nearest-row cosine quantiles [0.649 0.71  0.796 0.922 0.991]
k 20 average coherence 0.692 cluster sizes [42, 38, 37, 37, 36, 30, 29, 28, 26, 26, 24, 24, 23, 21, 21, 20, 19, 18, 18, 14] coherence [0.58 0.59 0.62 0.63 0.64 0.66 0.66 0.67 0.7  0.7  0.71 0.71 0.72 0.73 0.74 0.76 0.76 0.76 0.79 0.84]
k 24 average coherence 0.723 cluster sizes [36, 35, 34, 27, 26, 25, 25, 24, 24, 22, 22, 21, 21, 20, 20, 19, 19, 19, 17, 17, 15, 15, 15, 13] coherence [0.63 0.64 0.65 0.66 0.66 0.68 0.68 0.68 0.7  0.7  0.71 0.73 0.73 0.73 0.75 0.75 0.76 0.76 0.78 0.79 0.79 0.81 0.81 0.85]
k 28 average coherence 0.746 cluster sizes [37, 32, 26, 25, 23, 21, 20, 20, 20, 20, 19, 19, 19, 18, 18, 18, 18, 18, 17, 17, 16, 16, 16, 14, 13, 12, 12, 7] coherence [0.66 0.67 0.68 0.69 0.7  0.7  0.7  0.7  0.72 0.72 0.73 0.73 0.74 0.75 0.75 0.75 0.76 0.76 0.77 0.77 0.77 0.77 0.78 0.8  0.8  0.81 0.84 0.89]
k 32 average coherence 0.759 cluster sizes [35, 33, 22, 22, 21, 20, 20, 19, 19, 18, 18, 18, 17, 17, 17, 16, 16, 16, 16, 15, 14, 13, 13, 13, 12, 11, 11, 11, 11, 10, 9, 8] coherence [0.62 0.67 0.69 0.7  0.7  0.7  0.7  0.7  0.71 0.72 0.72 0.73 0.74 0.74 0.75 0.76 0.76 0.77 0.77 0.78 0.78 0.78 0.78 0.8  0.81 0.82 0.83 0.83 0.84
 0.85 0.87 0.88]

Projected FC0 rank 24 active 531 nearest-row cosine quantiles [0.629 0.698 0.792 0.928 0.993]
k 20 average coherence 0.688 cluster sizes [55, 43, 40, 33, 31, 30, 27, 25, 25, 24, 23, 22, 21, 21, 21, 20, 19, 19, 18, 14] coherence [0.54 0.55 0.62 0.63 0.65 0.68 0.68 0.69 0.69 0.7  0.7  0.71 0.73 0.73 0.74 0.75 0.75 0.75 0.76 0.86]
k 24 average coherence 0.718 cluster sizes [56, 37, 30, 29, 29, 25, 24, 23, 23, 22, 22, 21, 21, 20, 19, 17, 17, 15, 15, 14, 14, 13, 13, 12] coherence [0.57 0.59 0.63 0.66 0.67 0.68 0.68 0.69 0.71 0.71 0.72 0.74 0.75 0.75 0.75 0.75 0.76 0.78 0.78 0.81 0.81 0.82 0.82 0.87]
k 28 average coherence 0.734 cluster sizes [49, 31, 29, 27, 25, 23, 22, 22, 22, 21, 20, 20, 20, 19, 18, 18, 16, 14, 14, 14, 14, 14, 12, 12, 12, 12, 8, 3] coherence [0.55 0.64 0.66 0.69 0.69 0.7  0.71 0.71 0.71 0.71 0.72 0.73 0.73 0.73 0.73 0.74 0.76 0.76 0.76 0.77 0.77 0.77 0.79 0.79 0.83 0.85 0.85 0.86]
k 32 average coherence 0.752 cluster sizes [50, 29, 24, 21, 21, 20, 20, 19, 18, 18, 17, 17, 17, 16, 16, 16, 16, 15, 15, 15, 14, 13, 13, 13, 13, 13, 12, 11, 10, 7, 6, 6] coherence [0.64 0.67 0.68 0.68 0.69 0.7  0.71 0.71 0.72 0.72 0.72 0.73 0.74 0.74 0.74 0.75 0.76 0.76 0.76 0.76 0.76 0.77 0.77 0.78 0.79 0.79 0.8  0.8  0.8
 0.84 0.87 0.87]

Projected FC0 rank 28 active 531 nearest-row cosine quantiles [0.625 0.696 0.792 0.931 0.993]
k 20 average coherence 0.671 cluster sizes [70, 52, 36, 29, 28, 28, 27, 25, 25, 24, 23, 22, 21, 20, 19, 18, 17, 17, 16, 14] coherence [0.5  0.51 0.56 0.63 0.63 0.64 0.65 0.66 0.68 0.69 0.7  0.72 0.72 0.72 0.74 0.74 0.75 0.78 0.8  0.87]
k 24 average coherence 0.707 cluster sizes [61, 35, 29, 27, 27, 26, 25, 24, 23, 22, 21, 21, 21, 21, 17, 16, 16, 15, 15, 15, 15, 13, 13, 13] coherence [0.53 0.58 0.6  0.63 0.64 0.69 0.7  0.7  0.71 0.72 0.73 0.73 0.74 0.74 0.75 0.75 0.75 0.75 0.75 0.76 0.76 0.81 0.82 0.87]
k 28 average coherence 0.732 cluster sizes [66, 27, 25, 22, 22, 21, 21, 20, 20, 20, 20, 19, 18, 17, 17, 17, 16, 15, 15, 14, 14, 14, 14, 13, 13, 13, 10, 8] coherence [0.57 0.63 0.65 0.65 0.69 0.69 0.69 0.7  0.71 0.72 0.73 0.73 0.73 0.73 0.74 0.74 0.74 0.76 0.76 0.76 0.77 0.78 0.78 0.79 0.82 0.82 0.83 0.87]
k 32 average coherence 0.747 cluster sizes [32, 27, 26, 24, 22, 21, 21, 21, 21, 19, 19, 18, 18, 18, 18, 17, 16, 16, 15, 14, 13, 12, 12, 12, 12, 12, 11, 11, 11, 9, 7, 6] coherence [0.66 0.67 0.67 0.67 0.68 0.68 0.69 0.7  0.71 0.72 0.73 0.73 0.73 0.74 0.74 0.74 0.75 0.75 0.75 0.75 0.75 0.76 0.76 0.77 0.79 0.8  0.8  0.82 0.86
 0.87 0.87 0.89]

Projected FC0 rank 32 active 531 nearest-row cosine quantiles [0.609 0.684 0.793 0.929 0.992]
k 20 average coherence 0.665 cluster sizes [65, 58, 30, 29, 28, 28, 27, 27, 25, 24, 24, 23, 20, 20, 19, 19, 18, 17, 16, 14] coherence [0.44 0.55 0.59 0.63 0.65 0.66 0.66 0.66 0.66 0.67 0.67 0.69 0.7  0.71 0.74 0.75 0.76 0.77 0.8  0.84]
k 24 average coherence 0.7 cluster sizes [46, 34, 31, 29, 28, 27, 26, 25, 25, 24, 23, 23, 23, 20, 20, 18, 17, 16, 16, 15, 13, 13, 12, 7] coherence [0.55 0.56 0.57 0.61 0.61 0.66 0.67 0.67 0.68 0.69 0.7  0.73 0.73 0.73 0.73 0.75 0.77 0.79 0.8  0.8  0.8  0.84 0.85 0.86]
k 28 average coherence 0.725 cluster sizes [43, 28, 28, 27, 26, 23, 22, 21, 21, 20, 20, 19, 19, 18, 17, 17, 16, 15, 15, 14, 14, 14, 14, 13, 13, 13, 12, 9] coherence [0.54 0.64 0.65 0.66 0.66 0.66 0.67 0.69 0.7  0.7  0.71 0.72 0.72 0.73 0.74 0.74 0.74 0.75 0.75 0.75 0.76 0.76 0.77 0.79 0.81 0.82 0.84 0.85]
k 32 average coherence 0.746 cluster sizes [62, 29, 28, 22, 22, 22, 19, 18, 18, 18, 17, 17, 16, 16, 16, 15, 14, 14, 13, 13, 13, 12, 12, 12, 11, 11, 11, 10, 9, 8, 7, 6] coherence [0.61 0.62 0.66 0.66 0.68 0.68 0.68 0.68 0.71 0.71 0.72 0.73 0.74 0.75 0.75 0.75 0.75 0.76 0.76 0.77 0.78 0.79 0.8  0.8  0.8  0.81 0.83 0.83 0.84
 0.85 0.9  0.92]

Final MLP output-column geometry in top 28 output directions:
k 20 average coherence 0.436 cluster sizes [89, 86, 84, 84, 83, 82, 81, 81, 81, 80, 79, 79, 77, 76, 76, 76, 72, 66, 56, 48] coherence [0.39 0.4  0.41 0.41 0.41 0.41 0.41 0.41 0.42 0.42 0.42 0.43 0.43 0.44 0.44 0.44 0.45 0.53 0.54 0.58]
k 24 average coherence 0.453 cluster sizes [81, 76, 74, 71, 71, 70, 69, 69, 68, 67, 67, 67, 66, 66, 64, 64, 63, 62, 60, 58, 52, 50, 49, 32] coherence [0.41 0.41 0.42 0.42 0.43 0.43 0.43 0.43 0.44 0.44 0.44 0.44 0.44 0.45 0.45 0.45 0.45 0.45 0.46 0.46 0.49 0.55 0.61 0.65]
k 28 average coherence 0.47 cluster sizes [69, 68, 64, 64, 63, 63, 61, 60, 59, 59, 58, 58, 57, 57, 57, 55, 55, 52, 52, 51, 51, 49, 48, 48, 46, 46, 38, 28] coherence [0.43 0.43 0.44 0.44 0.44 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.46 0.46 0.46 0.46 0.47 0.47 0.47 0.48 0.48 0.49 0.49 0.49 0.51 0.61 0.68]
k 32 average coherence 0.483 cluster sizes [60, 58, 58, 57, 56, 55, 55, 54, 53, 53, 52, 52, 51, 51, 49, 49, 49, 48, 46, 44, 44, 43, 42, 41, 41, 41, 41, 40, 40, 40, 38, 35] coherence [0.44 0.44 0.45 0.45 0.45 0.45 0.46 0.46 0.46 0.46 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.48 0.48 0.48 0.49 0.49 0.49 0.5  0.5  0.51 0.51
 0.55 0.63 0.65]
k 40 average coherence 0.504 cluster sizes [46, 45, 44, 44, 44, 44, 44, 44, 43, 42, 41, 41, 41, 40, 40, 40, 40, 39, 39, 39, 38, 38, 38, 38, 38, 38, 37, 36, 36, 36, 36, 35, 35, 34, 32, 32, 32, 29, 29, 29] coherence [0.47 0.47 0.47 0.47 0.48 0.48 0.48 0.48 0.48 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.5  0.5  0.5  0.5  0.51
 0.51 0.51 0.51 0.51 0.51 0.51 0.52 0.53 0.64 0.65 0.67]

```