OUTPUT of run 8 of at most 100:
```
L0 position-subspace bilinear forms versus powers of the H5 polar factor
Power columns: [-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8]
L0H0 [ 0.027 -0.106 -0.067 -0.135  0.054  0.035  0.105 -0.012  0.02  -0.116
 -0.007 -0.033]
L0H1 [-0.43  -0.111  0.29  -0.29  -0.031  0.647 -0.016 -0.335  0.197 -0.036
 -0.257  0.24 ]
L0H2 [-0.113  0.119  0.157  0.023  0.034 -0.131 -0.213 -0.056  0.091  0.1
  0.185  0.054]
L0H3 [ 0.084  0.027 -0.152 -0.302 -0.123  0.03   0.086  0.211  0.138 -0.098
 -0.132 -0.093]
L0H4 [-0.083 -0.033  0.168 -0.253  0.03   0.08  -0.086 -0.026  0.173 -0.177
  0.087  0.046]
L0H5 [-0.08   0.027 -0.328  0.18   0.956  0.18  -0.328  0.027 -0.08  -0.291
  0.176  0.11 ]

Matching geometry restricted to initial shared value-reading subspace
For U.T QK_l OV_0H5 U: trace/Frobenius, trace/nuclear, symmetric fraction, largest eigenvalues
L1H0 -0.282 -0.081 0.554 [-0.07 +0.j    -0.056+0.j     0.051+0.j    -0.034+0.034j]
L1H1 0.685 0.193 0.555 [0.256+0.j    0.162+0.j    0.012+0.118j 0.012-0.118j]
L1H2 -0.241 -0.066 0.565 [-0.105+0.j    -0.073+0.012j -0.073-0.012j  0.069+0.j   ]
L1H3 0.554 0.155 0.582 [ 0.134+0.036j  0.134-0.036j -0.138+0.j     0.082+0.066j]
L1H4 0.437 0.123 0.564 [-0.115+0.j     0.098+0.046j  0.098-0.046j  0.074+0.j   ]
L1H5 0.513 0.152 0.613 [0.35 +0.j    0.153+0.j    0.016+0.097j 0.016-0.097j]
L2H0 -0.229 -0.059 0.506 [-0.174+0.j    -0.082+0.108j -0.082-0.108j  0.128+0.j   ]
L2H1 2.954 0.755 0.766 [0.412+0.j    0.381+0.139j 0.381-0.139j 0.37 +0.024j]
L2H2 -1.807 -0.476 0.624 [-0.396+0.2j   -0.396-0.2j   -0.357+0.j    -0.263+0.175j]
L2H3 -0.194 -0.049 0.527 [ 0.169+0.j    -0.144+0.j     0.038+0.119j  0.038-0.119j]
L2H4 0.039 0.01 0.555 [ 0.192+0.j    -0.136+0.026j -0.136-0.026j -0.083+0.103j]
L2H5 0.485 0.125 0.53 [0.106+0.013j 0.106-0.013j 0.009+0.09j  0.009-0.09j ]
L3H0 1.353 0.343 0.62 [0.27 +0.j    0.225+0.j    0.17 +0.067j 0.17 -0.067j]
L3H1 2.764 0.698 0.711 [0.32 +0.j    0.293+0.j    0.234+0.067j 0.234-0.067j]
L3H2 -0.095 -0.024 0.515 [-0.131+0.048j -0.131-0.048j  0.109+0.084j  0.109-0.084j]
L3H3 0.039 0.01 0.488 [-0.02 +0.057j -0.02 -0.057j  0.051+0.021j  0.051-0.021j]
L3H4 0.603 0.155 0.523 [0.11 +0.042j 0.11 -0.042j 0.099+0.j    0.034+0.085j]
L3H5 2.947 0.753 0.753 [0.468+0.015j 0.468-0.015j 0.359+0.111j 0.359-0.111j]

QK affinity of L1 heads: pairwise Frobenius cosines
[[1.    0.302 0.393 0.327 0.338 0.266]
 [0.302 1.    0.524 0.591 0.568 0.566]
 [0.393 0.524 1.    0.538 0.578 0.45 ]
 [0.327 0.591 0.538 1.    0.607 0.524]
 [0.338 0.568 0.578 0.607 1.    0.479]
 [0.266 0.566 0.45  0.524 0.479 1.   ]]

Direct positional-weight overlap at later layers
L1H0 best polar power 1 cosine 0.054 at powers 0,1,2 [0.004 0.054 0.038]
L1H1 best polar power 2 cosine 0.077 at powers 0,1,2 [-0.074 -0.003  0.077]
L1H2 best polar power 3 cosine 0.081 at powers 0,1,2 [-0.052  0.018  0.063]
L1H3 best polar power 2 cosine 0.064 at powers 0,1,2 [-0.068 -0.004  0.064]
L1H4 best polar power 2 cosine 0.101 at powers 0,1,2 [-0.05  -0.024  0.101]
L1H5 best polar power 2 cosine 0.094 at powers 0,1,2 [-0.109 -0.048  0.094]
L2H0 best polar power 1 cosine 0.103 at powers 0,1,2 [-0.01   0.103  0.012]
L2H1 best polar power 0 cosine 0.331 at powers 0,1,2 [0.331 0.    0.026]
L2H2 best polar power 0 cosine 0.192 at powers 0,1,2 [ 0.192  0.022 -0.079]
L2H3 best polar power 1 cosine 0.076 at powers 0,1,2 [0.022 0.076 0.046]
L2H4 best polar power 0 cosine 0.047 at powers 0,1,2 [0.047 0.01  0.017]
L2H5 best polar power 8 cosine 0.054 at powers 0,1,2 [ 0.007 -0.082  0.04 ]
L3H0 best polar power 0 cosine 0.161 at powers 0,1,2 [ 0.161 -0.026 -0.003]
L3H1 best polar power 0 cosine 0.258 at powers 0,1,2 [ 0.258  0.073 -0.103]
L3H2 best polar power 0 cosine 0.115 at powers 0,1,2 [0.115 0.018 0.015]
L3H3 best polar power 2 cosine 0.083 at powers 0,1,2 [-0.065 -0.048  0.083]
L3H4 best polar power 8 cosine 0.046 at powers 0,1,2 [-0.035  0.004  0.028]
L3H5 best polar power 0 cosine 0.589 at powers 0,1,2 [ 0.589  0.011 -0.083]

```