OUTPUT of run 2 of at most 100:
```
L0 ln1_w: largest 45 coordinates
[(211, 1.0134), (273, 0.9813), (223, 0.9731), (180, 0.9483), (50, 0.9335), (162, 0.9129), (60, 0.9031), (228, 0.9005), (48, 0.8725), (307, 0.8441), (359, 0.8331), (184, 0.8285), (240, 0.8178), (125, 0.8091), (132, 0.8068), (169, 0.8059), (314, 0.7991), (317, 0.7904), (300, 0.7823), (152, 0.7762), (158, 0.773), (246, 0.7606), (256, 0.7391), (59, 0.7363), (351, 0.7351), (356, 0.7144), (191, 0.6965), (224, 0.6901), (102, 0.6864), (15, 0.6845), (178, 0.6671), (151, 0.654), (320, 0.6535), (12, 0.6526), (136, 0.6417), (56, 0.6349), (239, 0.6336), (207, 0.6255), (35, 0.6168), (21, 0.6076), (28, 0.5958), (373, 0.5931), (360, 0.5884), (47, 0.5863), (204, 0.5858)]

Effective QK spectra and largest-magnitude eigenvalues
L0H0 norm 0.91 SV [0.709 0.541 0.106 0.064 0.045 0.04  0.033 0.033] eig [-0.392+0.j     0.048+0.069j  0.048-0.069j -0.023+0.j    -0.009+0.013j
 -0.009-0.013j -0.013+0.002j -0.013-0.002j] symfrac 0.591
L0H1 norm 7.02 SV [4.811 2.985 2.375 1.692 1.591 1.239 1.142 0.718] eig [ 1.742+2.761j  1.742-2.761j -2.275+0.j    -0.985+1.196j -0.985-1.196j
 -0.778+0.784j -0.778-0.784j -0.254-0.33j ] symfrac 0.45
L0H2 norm 1.396 SV [1.056 0.638 0.35  0.247 0.224 0.202 0.169 0.147] eig [ 0.725+0.j     0.426+0.j    -0.176+0.j    -0.106+0.006j -0.106-0.006j
  0.091+0.j    -0.08 +0.j    -0.045+0.033j] symfrac 0.701
L0H3 norm 1.916 SV [1.316 1.12  0.649 0.249 0.234 0.169 0.147 0.132] eig [-0.62 +0.044j -0.62 -0.044j -0.159+0.j     0.048+0.133j  0.048-0.133j
  0.06 +0.j    -0.049+0.013j -0.049-0.013j] symfrac 0.605
L0H4 norm 0.074 SV [0.036 0.022 0.02  0.016 0.016 0.015 0.013 0.013] eig [-0.01 +0.005j -0.01 -0.005j -0.004+0.004j -0.004-0.004j  0.001+0.005j
  0.001-0.005j -0.005+0.j     0.005+0.j   ] symfrac 0.512
L0H5 norm 7.764 SV [3.279 2.892 2.188 2.032 1.958 1.78  1.726 1.636] eig [1.656+2.197j 1.656-2.197j 0.911+1.375j 0.911-1.375j 1.427+0.j
 1.237+0.675j 1.237-0.675j 0.278+1.326j] symfrac 0.386
L1H0 norm 5.152 SV [2.83  2.014 1.745 1.34  1.261 1.111 0.964 0.946] eig [ 0.226+0.41j   0.226-0.41j  -0.41 +0.186j -0.41 -0.186j -0.406+0.j
 -0.328+0.106j -0.328-0.106j -0.334+0.j   ] symfrac 0.51
L1H1 norm 12.675 SV [9.164 5.291 3.674 2.61  1.989 1.719 1.705 1.488] eig [ 0.642+2.083j  0.642-2.083j -1.152+0.068j -1.152-0.068j -0.74 +0.631j
 -0.74 -0.631j -0.816+0.j    -0.794+0.153j] symfrac 0.498
L1H2 norm 9.886 SV [6.455 5.544 2.657 1.642 1.444 1.27  1.219 1.143] eig [ 0.457+1.616j  0.457-1.616j -0.864+0.j    -0.559+0.397j -0.559-0.397j
 -0.628+0.036j -0.628-0.036j -0.511+0.j   ] symfrac 0.492
L1H3 norm 10.475 SV [7.302 5.595 2.473 1.619 1.423 1.339 1.2   1.157] eig [ 0.609+2.177j  0.609-2.177j -0.755+0.j     0.735+0.j    -0.64 +0.193j
 -0.64 -0.193j -0.615+0.j    -0.576+0.j   ] symfrac 0.478
L1H4 norm 9.993 SV [6.784 5.233 2.719 1.705 1.53  1.294 1.237 1.209] eig [ 0.567+1.91j   0.567-1.91j  -0.677+0.113j -0.677-0.113j -0.621+0.j
 -0.516+0.225j -0.516-0.225j -0.556+0.j   ] symfrac 0.481
L1H5 norm 11.691 SV [8.071 4.438 3.852 3.6   1.939 1.717 1.585 1.367] eig [ 0.577+1.634j  0.577-1.634j -1.251+0.j    -0.988+0.j    -0.662+0.422j
 -0.662-0.422j -0.641-0.242j -0.641+0.242j] symfrac 0.505
L2H0 norm 16.364 SV [4.147 3.88  3.67  3.328 3.255 3.174 3.11  3.023] eig [ 0.263+1.058j  0.263-1.058j -0.936+0.j     0.724+0.593j  0.724-0.593j
  0.295+0.832j  0.295-0.832j -0.823-0.248j] symfrac 0.499
L2H1 norm 15.563 SV [3.666 3.366 3.17  3.148 2.939 2.838 2.819 2.757] eig [1.137-0.284j 1.137+0.284j 1.136+0.j    1.128-0.088j 1.128+0.088j
 1.051-0.175j 1.051+0.175j 0.821+0.634j] symfrac 0.52
L2H2 norm 22.432 SV [5.671 5.545 5.406 5.075 4.889 4.782 4.468 4.387] eig [ 2.069+0.j     0.637+1.729j  0.637-1.729j  1.544+0.466j  1.544-0.466j
  1.558+0.206j  1.558-0.206j -1.377+0.178j] symfrac 0.516
L2H3 norm 15.807 SV [4.566 3.385 3.295 3.137 3.103 2.964 2.914 2.856] eig [ 0.46 +1.476j  0.46 -1.476j  0.012+0.849j  0.012-0.849j -0.437+0.683j
 -0.437-0.683j  0.774+0.209j  0.774-0.209j] symfrac 0.494
L2H4 norm 17.612 SV [6.262 4.697 3.875 3.435 3.333 3.211 3.179 3.08 ] eig [ 0.643+1.761j  0.643-1.761j  1.229+0.j    -0.967+0.j     0.685+0.612j
  0.685-0.612j -0.886+0.227j -0.886-0.227j] symfrac 0.5
L2H5 norm 13.233 SV [3.355 3.314 2.873 2.56  2.517 2.371 2.35  2.307] eig [-0.854+0.j    -0.053+0.811j -0.053-0.811j -0.636+0.362j -0.636-0.362j
  0.723+0.j    -0.536+0.441j -0.536-0.441j] symfrac 0.497
L3H0 norm 16.621 SV [3.243 3.192 3.08  3.013 2.922 2.872 2.846 2.781] eig [1.044+0.j    0.948-0.317j 0.948+0.317j 0.954-0.142j 0.954+0.142j
 0.87 +0.j    0.13 +0.838j 0.13 -0.838j] symfrac 0.51
L3H1 norm 13.558 SV [2.578 2.516 2.469 2.429 2.398 2.363 2.321 2.249] eig [0.877+0.22j  0.877-0.22j  0.897+0.j    0.602+0.57j  0.602-0.57j
 0.819+0.j    0.696+0.322j 0.696-0.322j] symfrac 0.511
L3H2 norm 16.487 SV [3.47  3.288 3.133 2.897 2.867 2.821 2.736 2.7  ] eig [0.286+0.912j 0.286-0.912j 0.909-0.207j 0.909+0.207j 0.022+0.878j
 0.022-0.878j 0.848+0.j    0.563-0.616j] symfrac 0.497
L3H3 norm 8.424 SV [2.099 1.898 1.662 1.617 1.547 1.527 1.436 1.391] eig [ 0.216+0.491j  0.216-0.491j  0.476+0.j     0.208+0.388j  0.208-0.388j
 -0.018+0.406j -0.018-0.406j -0.335+0.205j] symfrac 0.496
L3H4 norm 13.875 SV [3.205 2.956 2.854 2.588 2.501 2.451 2.351 2.32 ] eig [-0.843+0.j     0.746+0.j     0.524+0.473j  0.524-0.473j  0.232+0.633j
  0.232-0.633j -0.018+0.666j -0.018-0.666j] symfrac 0.502
L3H5 norm 16.935 SV [3.233 3.119 3.073 2.957 2.918 2.897 2.879 2.78 ] eig [1.556+0.937j 1.556-0.937j 1.702+0.591j 1.702-0.591j 1.599+0.83j
 1.599-0.83j  1.615+0.609j 1.615-0.609j] symfrac 0.611

Full singular spectra at selected quantiles
W_fc 0 [(1, np.float64(18.11)), (2, np.float64(12.28)), (3, np.float64(8.473)), (4, np.float64(7.902)), (5, np.float64(7.779)), (6, np.float64(7.442)), (10, np.float64(6.805)), (15, np.float64(6.27)), (20, np.float64(5.944)), (25, np.float64(5.609)), (26, np.float64(5.58)), (27, np.float64(5.498)), (28, np.float64(5.447)), (29, np.float64(5.377)), (30, np.float64(5.334)), (32, np.float64(5.203)), (40, np.float64(4.716)), (50, np.float64(4.081)), (64, np.float64(3.281)), (80, np.float64(2.205)), (100, np.float64(1.622)), (128, np.float64(1.264)), (192, np.float64(0.94)), (256, np.float64(0.75)), (320, np.float64(0.596)), (384, np.float64(0.421))]
W_proj 0 [(1, np.float64(10.932)), (2, np.float64(7.576)), (3, np.float64(6.628)), (4, np.float64(6.293)), (5, np.float64(6.166)), (6, np.float64(5.924)), (10, np.float64(5.61)), (15, np.float64(5.193)), (20, np.float64(4.937)), (25, np.float64(4.651)), (26, np.float64(4.637)), (27, np.float64(4.548)), (28, np.float64(4.526)), (29, np.float64(4.487)), (30, np.float64(4.404)), (32, np.float64(4.283)), (40, np.float64(4.023)), (50, np.float64(3.694)), (64, np.float64(3.268)), (80, np.float64(2.868)), (100, np.float64(2.413)), (128, np.float64(1.936)), (192, np.float64(1.172)), (256, np.float64(0.708)), (320, np.float64(0.432)), (384, np.float64(0.244))]
W_fc 3 [(1, np.float64(14.373)), (2, np.float64(8.176)), (3, np.float64(7.973)), (4, np.float64(7.83)), (5, np.float64(7.036)), (6, np.float64(6.757)), (10, np.float64(6.387)), (15, np.float64(6.162)), (20, np.float64(5.895)), (25, np.float64(5.753)), (26, np.float64(5.699)), (27, np.float64(5.681)), (28, np.float64(5.652)), (29, np.float64(5.641)), (30, np.float64(5.641)), (32, np.float64(5.564)), (40, np.float64(5.357)), (50, np.float64(5.178)), (64, np.float64(4.945)), (80, np.float64(4.733)), (100, np.float64(4.483)), (128, np.float64(4.184)), (192, np.float64(3.606)), (256, np.float64(3.093)), (320, np.float64(2.545)), (384, np.float64(0.708))]
W_proj 3 [(1, np.float64(28.175)), (2, np.float64(20.293)), (3, np.float64(19.292)), (4, np.float64(19.135)), (5, np.float64(18.708)), (6, np.float64(18.57)), (10, np.float64(16.54)), (15, np.float64(14.417)), (20, np.float64(12.37)), (25, np.float64(10.769)), (26, np.float64(9.227)), (27, np.float64(8.573)), (28, np.float64(7.929)), (29, np.float64(6.5)), (30, np.float64(5.271)), (32, np.float64(3.184)), (40, np.float64(2.29)), (50, np.float64(1.926)), (64, np.float64(1.692)), (80, np.float64(1.508)), (100, np.float64(1.319)), (128, np.float64(1.138)), (192, np.float64(0.832)), (256, np.float64(0.632)), (320, np.float64(0.481)), (384, np.float64(0.324))]

L0 QK pairwise Frobenius cosine
[[ 1.     0.179  0.112  0.206  0.063  0.093]
 [ 0.179  1.     0.21  -0.15   0.005  0.414]
 [ 0.112  0.21   1.    -0.247 -0.006  0.114]
 [ 0.206 -0.15  -0.247  1.    -0.027 -0.098]
 [ 0.063  0.005 -0.006 -0.027  1.    -0.004]
 [ 0.093  0.414  0.114 -0.098 -0.004  1.   ]]

Weight-only key-composition enrichment
For later head B and earlier head A: ||QK_B OV_A||_F / (||QK_B||_F ||OV_A||_F/sqrt(384)).
L1H0 [('L0H4', np.float64(7.74)), ('L0H0', np.float64(6.237)), ('L0H3', np.float64(2.815)), ('L0H2', np.float64(1.686)), ('L0H5', np.float64(1.307)), ('L0H1', np.float64(1.109))]
L1H1 [('L0H4', np.float64(10.672)), ('L0H0', np.float64(8.436)), ('L0H3', np.float64(3.299)), ('L0H2', np.float64(2.049)), ('L0H5', np.float64(1.007)), ('L0H1', np.float64(0.58))]
L1H2 [('L0H4', np.float64(10.165)), ('L0H0', np.float64(8.084)), ('L0H3', np.float64(3.365)), ('L0H2', np.float64(1.976)), ('L0H5', np.float64(0.944)), ('L0H1', np.float64(0.611))]
L1H3 [('L0H4', np.float64(10.707)), ('L0H0', np.float64(8.609)), ('L0H3', np.float64(3.634)), ('L0H2', np.float64(2.128)), ('L0H5', np.float64(0.957)), ('L0H1', np.float64(0.567))]
L1H4 [('L0H4', np.float64(10.328)), ('L0H0', np.float64(8.356)), ('L0H3', np.float64(3.51)), ('L0H2', np.float64(2.123)), ('L0H5', np.float64(1.02)), ('L0H1', np.float64(0.592))]
L1H5 [('L0H4', np.float64(9.908)), ('L0H0', np.float64(7.846)), ('L0H3', np.float64(2.812)), ('L0H2', np.float64(1.79)), ('L0H5', np.float64(1.195)), ('L0H1', np.float64(0.664))]
L2H0 [('L0H4', np.float64(3.137)), ('L0H0', np.float64(2.5)), ('L0H3', np.float64(1.296)), ('L1H0', np.float64(1.277)), ('L0H5', np.float64(1.233)), ('L0H2', np.float64(1.227))]
L2H1 [('L0H5', np.float64(1.492)), ('L1H3', np.float64(1.389)), ('L1H2', np.float64(1.355)), ('L1H4', np.float64(1.349)), ('L1H0', np.float64(1.3)), ('L1H1', np.float64(1.259))]
L2H2 [('L0H4', np.float64(3.585)), ('L0H0', np.float64(2.872)), ('L0H3', np.float64(1.499)), ('L0H5', np.float64(1.384)), ('L1H0', np.float64(1.2)), ('L0H2', np.float64(1.176))]
L2H3 [('L0H4', np.float64(4.201)), ('L0H0', np.float64(3.344)), ('L0H3', np.float64(1.71)), ('L0H2', np.float64(1.236)), ('L0H5', np.float64(1.171)), ('L1H0', np.float64(1.158))]
L2H4 [('L0H4', np.float64(4.245)), ('L0H0', np.float64(3.401)), ('L0H2', np.float64(1.808)), ('L0H3', np.float64(1.718)), ('L1H0', np.float64(1.584)), ('L0H5', np.float64(1.195))]
L2H5 [('L0H4', np.float64(2.867)), ('L0H0', np.float64(2.252)), ('L0H2', np.float64(1.27)), ('L0H3', np.float64(1.134)), ('L1H0', np.float64(1.123)), ('L0H5', np.float64(1.057))]
L3H0 [('L0H4', np.float64(1.839)), ('L0H0', np.float64(1.405)), ('L0H2', np.float64(1.145)), ('L0H5', np.float64(1.113)), ('L1H0', np.float64(1.108)), ('L1H2', np.float64(1.04))]
L3H1 [('L0H5', np.float64(1.359)), ('L0H4', np.float64(1.222)), ('L2H2', np.float64(1.201)), ('L1H2', np.float64(1.178)), ('L1H4', np.float64(1.16)), ('L0H2', np.float64(1.137))]
L3H2 [('L0H4', np.float64(2.236)), ('L0H0', np.float64(1.658)), ('L0H2', np.float64(1.108)), ('L0H5', np.float64(1.088)), ('L1H0', np.float64(1.076)), ('L1H4', np.float64(1.004))]
L3H3 [('L0H4', np.float64(1.282)), ('L0H2', np.float64(1.135)), ('L2H1', np.float64(1.099)), ('L1H0', np.float64(1.099)), ('L0H0', np.float64(1.076)), ('L1H4', np.float64(1.025))]
L3H4 [('L0H4', np.float64(2.286)), ('L0H0', np.float64(1.736)), ('L0H2', np.float64(1.144)), ('L1H0', np.float64(1.106)), ('L1H2', np.float64(1.034)), ('L2H5', np.float64(0.99))]
L3H5 [('L0H5', np.float64(1.534)), ('L2H2', np.float64(1.477)), ('L1H3', np.float64(1.38)), ('L1H4', np.float64(1.368)), ('L2H3', np.float64(1.347)), ('L1H2', np.float64(1.345))]

```