OUTPUT of run 3 of at most 100:
```
Layer 0 scaled QK: symmetric-energy fraction, positive/negative eigenvalue sums of symmetric part
H 0 [ 0.5704  0.3783 -0.483 ]
eigenvalues: [ 0.0796+0.j      0.0483+0.j     -0.024 +0.0057j -0.024 -0.0057j -0.0226+0.j      0.0176+0.0134j  0.0176-0.0134j -0.0201+0.j     -0.0138-0.0121j
 -0.0138+0.0121j -0.0139-0.0031j -0.0139+0.0031j -0.0137+0.j     -0.011 -0.0039j -0.011 +0.0039j -0.0111+0.0023j -0.0111-0.0023j -0.006 -0.0062j
 -0.006 +0.0062j -0.0063+0.j     -0.003 -0.0049j -0.003 +0.0049j -0.0052-0.0023j -0.0052+0.0023j]
H 1 [ 0.5805  0.1152 -0.2136]
eigenvalues: [-0.0619+0.j     -0.01  +0.j     -0.0089+0.j      0.0043+0.j     -0.0039+0.j     -0.0033-0.0018j -0.0033+0.0018j -0.0017+0.0004j -0.0017-0.0004j
 -0.0016-0.0007j -0.0016+0.0007j -0.0011+0.0003j -0.0011-0.0003j -0.0007+0.0008j -0.0007-0.0008j  0.001 +0.j     -0.0009+0.j      0.0004+0.0007j
  0.0004-0.0007j -0.0007-0.0005j -0.0007+0.0005j -0.0005-0.0007j -0.0005+0.0007j -0.0002-0.0007j]
H 2 [ 0.6443  0.0809 -0.1682]
eigenvalues: [-0.0566+0.j     -0.0074-0.0027j -0.0074+0.0027j -0.0034-0.0008j -0.0034+0.0008j -0.0025+0.j     -0.0013-0.0003j -0.0013+0.0003j -0.0006-0.0012j
 -0.0006+0.0012j  0.0006+0.001j   0.0006-0.001j  -0.0003-0.001j  -0.0003+0.001j  -0.001 +0.j      0.0001+0.001j   0.0001-0.001j  -0.0005-0.0008j
 -0.0005+0.0008j -0.0007+0.0006j -0.0007-0.0006j  0.0008+0.j     -0.0006-0.0004j -0.0006+0.0004j]
H 3 [ 0.4664  1.9585 -0.617 ]
eigenvalues: [ 0.1366+0.1327j  0.1366-0.1327j  0.1099+0.0891j  0.1099-0.0891j  0.095 +0.0979j  0.095 -0.0979j  0.0841+0.1041j  0.0841-0.1041j  0.0644+0.1142j
  0.0644-0.1142j  0.0957-0.0687j  0.0957+0.0687j  0.0114+0.1166j  0.0114-0.1166j  0.1116+0.j      0.0559+0.0696j  0.0559-0.0696j  0.0749+0.0468j
  0.0749-0.0468j  0.0135-0.0747j  0.0135+0.0747j -0.0348-0.0526j -0.0348+0.0526j -0.0451+0.0173j]
H 4 [ 0.5251  0.103  -0.1489]
eigenvalues: [-0.0152+0.j     -0.0095+0.j     -0.0077+0.j     -0.0026-0.0003j -0.0026+0.0003j -0.0022-0.0014j -0.0022+0.0014j -0.0002+0.0023j -0.0002-0.0023j
 -0.0014-0.0012j -0.0014+0.0012j -0.0015+0.j     -0.0006-0.0011j -0.0006+0.0011j  0.0008-0.0009j  0.0008+0.0009j  0.0012+0.j     -0.0003-0.0011j
 -0.0003+0.0011j  0.0005-0.0009j  0.0005+0.0009j -0.001 +0.j      0.001 +0.j     -0.0009-0.0001j]
H 5 [ 0.5122  0.0451 -0.0536]
eigenvalues: [-0.0049+0.j      0.0013+0.j     -0.0012+0.j     -0.0004-0.0007j -0.0004+0.0007j -0.0008+0.j     -0.0007+0.0002j -0.0007-0.0002j  0.0002-0.0007j
  0.0002+0.0007j -0.0001-0.0006j -0.0001+0.0006j -0.0003-0.0005j -0.0003+0.0005j  0.0002-0.0006j  0.0002+0.0006j -0.0005-0.0003j -0.0005+0.0003j
  0.0006+0.j     -0.0005+0.0001j -0.0005-0.0001j  0.0005+0.0001j  0.0005-0.0001j -0.0004+0.0004j]

Fraction of each OV's squared norm captured by QK H3 right/left subspaces
rank 4 key [0.007 0.441 0.562 0.012 0.362 0.826] query [0.025 0.484 0.585 0.011 0.354 0.697]
rank 8 key [0.014 0.462 0.584 0.027 0.374 0.853] query [0.033 0.503 0.612 0.026 0.382 0.732]
rank 16 key [0.025 0.48  0.608 0.06  0.413 0.882] query [0.043 0.528 0.646 0.054 0.422 0.767]
rank 24 key [0.037 0.503 0.625 0.085 0.445 0.898] query [0.058 0.577 0.679 0.074 0.487 0.782]
rank 32 key [0.071 0.525 0.64  0.112 0.475 0.907] query [0.095 0.679 0.727 0.089 0.645 0.811]
rank 48 key [0.263 0.605 0.707 0.29  0.551 0.924] query [0.288 0.831 0.844 0.25  0.787 0.887]

Own-head QK/OV subspace overlaps (r=1,4,8,16,24):
H 0 [[0.003 0.   ]
 [0.081 0.117]
 [0.073 0.093]
 [0.092 0.113]
 [0.15  0.168]]
H 1 [[0.175 0.078]
 [0.267 0.106]
 [0.188 0.106]
 [0.153 0.142]
 [0.162 0.162]]
H 2 [[0.011 0.071]
 [0.263 0.112]
 [0.206 0.118]
 [0.159 0.135]
 [0.175 0.166]]
H 3 [[0.    0.002]
 [0.005 0.004]
 [0.01  0.011]
 [0.02  0.024]
 [0.116 0.133]]
H 4 [[0.437 0.049]
 [0.191 0.058]
 [0.144 0.073]
 [0.136 0.121]
 [0.153 0.166]]
H 5 [[0.356 0.   ]
 [0.248 0.057]
 [0.171 0.093]
 [0.142 0.106]
 [0.152 0.132]]

Layer 0 cross-head subspace overlap: top 8 query and key directions
query [[1.    0.217 0.215 0.332 0.189 0.157]
 [0.217 1.    0.488 0.12  0.419 0.123]
 [0.215 0.488 1.    0.143 0.35  0.126]
 [0.332 0.12  0.143 1.    0.111 0.101]
 [0.189 0.419 0.35  0.111 1.    0.113]
 [0.157 0.123 0.126 0.101 0.113 1.   ]]
key [[1.    0.063 0.1   0.396 0.057 0.055]
 [0.063 1.    0.314 0.045 0.284 0.149]
 [0.1   0.314 1.    0.086 0.262 0.1  ]
 [0.396 0.045 0.086 1.    0.066 0.049]
 [0.057 0.284 0.262 0.066 1.    0.11 ]
 [0.055 0.149 0.1   0.049 0.11  1.   ]]

QK H3 singular-vector pair cosines:
[ 0.659  0.672  0.628  0.554  0.591  0.676  0.613  0.626  0.534  0.529  0.284  0.322  0.609  0.418  0.485  0.466  0.475  0.561 -0.393  0.188  0.043
 -0.121 -0.028  0.082 -0.117 -0.37  -0.159 -0.266  0.092 -0.442 -0.19  -0.313]
SV [0.2435 0.2224 0.2012 0.1816 0.1785 0.1571 0.1545 0.149  0.1401 0.1358 0.1306 0.1277 0.1195 0.1183 0.1151 0.1077 0.1034 0.0998 0.0909 0.0864 0.0823
 0.0767 0.0721 0.0691 0.0591 0.0552 0.0494 0.0464 0.0384 0.0308 0.0295 0.0268 0.0228 0.0216 0.0189 0.017  0.0163 0.0139 0.0131 0.0118]

L0 LN scale largest and smallest coordinates:
[(180, 0.9785), (184, 0.974), (162, 0.9704), (99, 0.9171), (211, 0.896), (256, 0.892), (300, 0.8045), (317, 0.804), (223, 0.8017), (39, 0.7989), (173, 0.7933), (4, 0.7864), (228, 0.7859), (69, 0.7721), (89, 0.7672), (100, 0.7658), (56, 0.753), (65, 0.7491), (354, 0.7465), (246, 0.7261), (124, 0.7207), (349, 0.7205), (60, 0.7127), (132, 0.7083)]
[(381, 0.0352), (42, 0.0606), (95, 0.0607), (17, 0.0622), (147, 0.0673), (237, 0.0678), (376, 0.0726), (334, 0.0736), (78, 0.075), (299, 0.0755), (233, 0.0756), (335, 0.0765), (81, 0.0775), (176, 0.0828), (340, 0.0844), (306, 0.0845), (230, 0.0847), (131, 0.0858), (263, 0.0886), (305, 0.0925), (156, 0.0951), (313, 0.0967), (282, 0.0972), (85, 0.0995)]

```