OUTPUT of run 3 of at most 100:
```
L0 QK eigenvalues, dominant invariant-space overlaps
H 0 rank95 10 L/R overlap 0.445 V energy in QK-left/right [0.057 0.082]
eigenvalues [ 0.08 +0.j     0.048+0.j    -0.024+0.006j -0.024-0.006j -0.023+0.j
  0.018+0.013j  0.018-0.013j -0.02 +0.j    -0.014+0.012j -0.014-0.012j
 -0.014+0.003j -0.014-0.003j -0.014+0.j    -0.011+0.004j -0.011-0.004j
 -0.011+0.002j]
H 1 rank95 2 L/R overlap 0.106 V energy in QK-left/right [0.199 0.043]
eigenvalues [-0.062+0.j    -0.01 +0.j    -0.009+0.j     0.004+0.j    -0.004+0.j
 -0.003+0.002j -0.003-0.002j -0.002+0.j    -0.002-0.j    -0.002+0.001j
 -0.002-0.001j -0.001-0.j    -0.001+0.j    -0.001-0.001j -0.001+0.001j
  0.001+0.j   ]
H 2 rank95 3 L/R overlap 0.268 V energy in QK-left/right [0.212 0.111]
eigenvalues [-0.057+0.j    -0.007+0.003j -0.007-0.003j -0.003+0.001j -0.003-0.001j
 -0.002+0.j    -0.001+0.j    -0.001-0.j    -0.001+0.001j -0.001-0.001j
  0.001+0.001j  0.001-0.001j -0.   +0.001j -0.   -0.001j -0.001+0.j
  0.   +0.001j]
H 3 rank95 23 L/R overlap 0.799 V energy in QK-left/right [0.143 0.165]
eigenvalues [0.137+0.133j 0.137-0.133j 0.11 +0.089j 0.11 -0.089j 0.095+0.098j
 0.095-0.098j 0.084+0.104j 0.084-0.104j 0.064+0.114j 0.064-0.114j
 0.096+0.069j 0.096-0.069j 0.011+0.117j 0.011-0.117j 0.112+0.j
 0.056-0.07j ]
H 4 rank95 5 L/R overlap 0.137 V energy in QK-left/right [0.175 0.055]
eigenvalues [-0.015+0.j    -0.01 +0.j    -0.008+0.j    -0.003+0.j    -0.003-0.j
 -0.002+0.001j -0.002-0.001j -0.   +0.002j -0.   -0.002j -0.001+0.001j
 -0.001-0.001j -0.002+0.j    -0.001-0.001j -0.001+0.001j  0.001-0.001j
  0.001+0.001j]
H 5 rank95 10 L/R overlap 0.105 V energy in QK-left/right [0.347 0.038]
eigenvalues [-0.005+0.j     0.001+0.j    -0.001+0.j    -0.   +0.001j -0.   -0.001j
 -0.001+0.j    -0.001+0.j    -0.001-0.j     0.   +0.001j  0.   -0.001j
 -0.   +0.001j -0.   -0.001j -0.   +0.001j -0.   -0.001j  0.   +0.001j
  0.   -0.001j]

QK-OV composition: trace(A_lh @ B_earlier)/(|A_lh| |B_earlier|)
L1H0 [0.002 0.034 0.05  0.006 0.029 0.048]
L1H1 [0.    0.006 0.025 0.014 0.004 0.021]
L1H2 [-0.002  0.03   0.042  0.012  0.031  0.047]
L1H3 [0.001 0.028 0.045 0.005 0.024 0.043]
L1H4 [0.001 0.017 0.03  0.001 0.023 0.037]
L1H5 [-0.001  0.019  0.04   0.011  0.019  0.031]
L2H0 [-0.     0.038  0.058  0.004  0.023  0.067  0.001  0.007  0.004  0.009
 -0.007  0.002]
L2H1 [ 0.001  0.021  0.033  0.001  0.013  0.042 -0.004 -0.009 -0.014 -0.009
 -0.015 -0.01 ]
L2H2 [ 0.003  0.026  0.039  0.005  0.014  0.046 -0.001  0.003 -0.001 -0.002
 -0.007  0.001]
L2H3 [ 0.003  0.016  0.023  0.005  0.012  0.025  0.002  0.002 -0.002 -0.
 -0.007 -0.004]
L2H4 [-0.001  0.03   0.045  0.009  0.022  0.051 -0.     0.002 -0.012 -0.015
 -0.003  0.002]
L2H5 [ 0.001  0.021  0.036  0.001  0.014  0.047 -0.009 -0.    -0.008 -0.007
 -0.007 -0.009]
L3H0 [-0.002  0.008  0.013 -0.01   0.005  0.013 -0.01  -0.008 -0.018 -0.013
 -0.012 -0.014 -0.008 -0.014 -0.019 -0.016 -0.036 -0.02 ]
L3H1 [ 0.002  0.01   0.013 -0.002  0.004  0.014 -0.006  0.002  0.003 -0.001
 -0.003  0.002 -0.009 -0.    -0.004  0.003 -0.002 -0.002]
L3H2 [-0.     0.007  0.012  0.002  0.001  0.004 -0.007 -0.001  0.    -0.
 -0.002 -0.001 -0.003 -0.001 -0.011 -0.008 -0.01  -0.005]
L3H3 [-0.008  0.002  0.002  0.063  0.002 -0.002  0.031  0.021  0.001 -0.003
 -0.019  0.027  0.028  0.033  0.009  0.013  0.022  0.048]
L3H4 [ 0.005  0.009  0.009  0.006  0.01   0.009  0.     0.002  0.002 -0.001
  0.005  0.002  0.008  0.009  0.014  0.009  0.012  0.009]
L3H5 [-0.     0.002  0.007 -0.003  0.     0.009 -0.012 -0.007 -0.005 -0.009
 -0.007 -0.007 -0.015 -0.016 -0.013 -0.013 -0.012 -0.01 ]

Strongest composition positivity, with nonrandom comparison
L1H0 [('L0H2', np.float64(0.134), np.float64(0.009), np.float64(0.376)), ('L0H5', np.float64(0.103), np.float64(0.002), np.float64(0.467)), ('L0H3', np.float64(0.102), np.float64(0.013), np.float64(0.057)), ('L0H4', np.float64(0.096), np.float64(0.013), np.float64(0.304))]
L1H1 [('L0H3', np.float64(0.218), np.float64(0.016), np.float64(0.065)), ('L0H2', np.float64(0.065), np.float64(0.005), np.float64(0.387)), ('L0H5', np.float64(0.043), np.float64(0.004), np.float64(0.489)), ('L0H1', np.float64(0.017), np.float64(0.005), np.float64(0.371))]
L1H2 [('L0H3', np.float64(0.168), np.float64(0.017), np.float64(0.072)), ('L0H2', np.float64(0.106), np.float64(0.006), np.float64(0.396)), ('L0H4', np.float64(0.1), np.float64(0.011), np.float64(0.313)), ('L0H5', np.float64(0.092), np.float64(0.002), np.float64(0.509))]
L1H3 [('L0H2', np.float64(0.113), np.float64(0.008), np.float64(0.4)), ('L0H5', np.float64(0.085), np.float64(0.002), np.float64(0.508)), ('L0H3', np.float64(0.076), np.float64(0.014), np.float64(0.068)), ('L0H4', np.float64(0.075), np.float64(0.014), np.float64(0.321))]
L1H4 [('L0H2', np.float64(0.079), np.float64(-0.0), np.float64(0.375)), ('L0H4', np.float64(0.078), np.float64(0.004), np.float64(0.297)), ('L0H5', np.float64(0.075), np.float64(-0.001), np.float64(0.494)), ('L0H1', np.float64(0.046), np.float64(-0.002), np.float64(0.36))]
L1H5 [('L0H3', np.float64(0.2), np.float64(0.029), np.float64(0.056)), ('L0H2', np.float64(0.102), np.float64(0.007), np.float64(0.387)), ('L0H5', np.float64(0.064), np.float64(0.003), np.float64(0.478)), ('L0H4', np.float64(0.062), np.float64(0.021), np.float64(0.314))]
L2H0 [('L1H3', np.float64(0.206), np.float64(-0.001), np.float64(0.045)), ('L0H2', np.float64(0.196), np.float64(0.027), np.float64(0.298)), ('L0H5', np.float64(0.193), np.float64(0.016), np.float64(0.345)), ('L1H1', np.float64(0.163), np.float64(0.003), np.float64(0.043))]
L2H1 [('L0H5', np.float64(0.199), np.float64(0.014), np.float64(0.214)), ('L0H2', np.float64(0.179), np.float64(0.023), np.float64(0.186)), ('L0H1', np.float64(0.117), np.float64(0.022), np.float64(0.18)), ('L0H4', np.float64(0.08), np.float64(0.023), np.float64(0.161))]
L2H2 [('L0H5', np.float64(0.186), np.float64(0.017), np.float64(0.248)), ('L0H2', np.float64(0.182), np.float64(0.027), np.float64(0.214)), ('L0H1', np.float64(0.124), np.float64(0.024), np.float64(0.208)), ('L0H3', np.float64(0.1), np.float64(0.0), np.float64(0.053))]
L2H3 [('L0H2', np.float64(0.129), np.float64(0.012), np.float64(0.174)), ('L0H5', np.float64(0.112), np.float64(0.007), np.float64(0.22)), ('L0H1', np.float64(0.097), np.float64(0.008), np.float64(0.168)), ('L0H4', np.float64(0.086), np.float64(0.007), np.float64(0.141))]
L2H4 [('L0H2', np.float64(0.186), np.float64(0.025), np.float64(0.243)), ('L0H5', np.float64(0.182), np.float64(0.015), np.float64(0.281)), ('L0H3', np.float64(0.16), np.float64(0.009), np.float64(0.055)), ('L0H1', np.float64(0.128), np.float64(0.021), np.float64(0.233))]
L2H5 [('L0H5', np.float64(0.212), np.float64(0.018), np.float64(0.224)), ('L0H2', np.float64(0.188), np.float64(0.021), np.float64(0.193)), ('L0H1', np.float64(0.113), np.float64(0.021), np.float64(0.187)), ('L0H4', np.float64(0.081), np.float64(0.025), np.float64(0.167))]
L3H0 [('L0H2', np.float64(0.107), np.float64(0.015), np.float64(0.119)), ('L0H5', np.float64(0.087), np.float64(0.004), np.float64(0.15)), ('L0H1', np.float64(0.069), np.float64(0.01), np.float64(0.117)), ('L0H4', np.float64(0.048), np.float64(0.014), np.float64(0.103))]
L3H1 [('L0H2', np.float64(0.093), np.float64(0.013), np.float64(0.144)), ('L0H5', np.float64(0.077), np.float64(0.005), np.float64(0.182)), ('L1H2', np.float64(0.073), np.float64(0.0), np.float64(0.046)), ('L0H1', np.float64(0.07), np.float64(0.014), np.float64(0.14))]
L3H2 [('L0H2', np.float64(0.081), np.float64(0.015), np.float64(0.147)), ('L0H1', np.float64(0.048), np.float64(0.014), np.float64(0.145)), ('L0H3', np.float64(0.034), np.float64(0.006), np.float64(0.051)), ('L0H5', np.float64(0.019), np.float64(0.005), np.float64(0.188))]
L3H3 [('L0H3', np.float64(0.924), np.float64(0.067), np.float64(0.068)), ('L2H5', np.float64(0.809), np.float64(0.013), np.float64(0.06)), ('L2H1', np.float64(0.563), np.float64(0.002), np.float64(0.058)), ('L1H0', np.float64(0.515), np.float64(0.001), np.float64(0.059))]
L3H4 [('L2H2', np.float64(0.281), np.float64(0.002), np.float64(0.051)), ('L2H4', np.float64(0.273), np.float64(0.006), np.float64(0.045)), ('L2H5', np.float64(0.203), np.float64(0.001), np.float64(0.046)), ('L0H4', np.float64(0.196), np.float64(0.022), np.float64(0.053))]
L3H5 [('L0H2', np.float64(0.05), np.float64(0.004), np.float64(0.146)), ('L0H5', np.float64(0.048), np.float64(0.001), np.float64(0.185)), ('L0H1', np.float64(0.017), np.float64(0.004), np.float64(0.142)), ('L0H4', np.float64(0.0), np.float64(0.01), np.float64(0.12))]

L0 value-subspace sharing and query/key orthogonality
Combined value singular values [3.339 2.305 1.516 0.814 0.773 0.711 0.682 0.672 0.651 0.633 0.618 0.597
 0.574 0.561 0.558 0.537 0.525 0.508 0.498 0.487 0.476 0.469 0.461 0.45
 0.432 0.427 0.417 0.41  0.408 0.395 0.388 0.382 0.38  0.376 0.363 0.359
 0.356 0.348 0.342 0.334 0.333 0.326 0.317 0.308 0.307]
value basis rank 2
H 0 Q/K/V energy [0.234 0.308 0.003]
H 1 Q/K/V energy [0.249 0.056 0.524]
H 2 Q/K/V energy [0.31 0.08 0.52]
H 3 Q/K/V energy [0.044 0.198 0.003]
H 4 Q/K/V energy [0.14  0.045 0.339]
H 5 Q/K/V energy [0.449 0.007 0.721]
value basis rank 10
H 0 Q/K/V energy [0.409 0.381 0.268]
H 1 Q/K/V energy [0.54  0.18  0.678]
H 2 Q/K/V energy [0.473 0.176 0.631]
H 3 Q/K/V energy [0.091 0.243 0.214]
H 4 Q/K/V energy [0.38  0.135 0.467]
H 5 Q/K/V energy [0.527 0.096 0.891]
value basis rank 20
H 0 Q/K/V energy [0.459 0.44  0.514]
H 1 Q/K/V energy [0.575 0.28  0.712]
H 2 Q/K/V energy [0.503 0.256 0.667]
H 3 Q/K/V energy [0.125 0.275 0.51 ]
H 4 Q/K/V energy [0.414 0.197 0.504]
H 5 Q/K/V energy [0.548 0.15  0.924]
value basis rank 28
H 0 Q/K/V energy [0.499 0.489 0.617]
H 1 Q/K/V energy [0.595 0.356 0.737]
H 2 Q/K/V energy [0.527 0.318 0.697]
H 3 Q/K/V energy [0.175 0.324 0.651]
H 4 Q/K/V energy [0.44  0.247 0.549]
H 5 Q/K/V energy [0.573 0.198 0.943]
value basis rank 40
H 0 Q/K/V energy [0.569 0.576 0.711]
H 1 Q/K/V energy [0.641 0.419 0.789]
H 2 Q/K/V energy [0.573 0.383 0.754]
H 3 Q/K/V energy [0.31  0.467 0.774]
H 4 Q/K/V energy [0.509 0.317 0.628]
H 5 Q/K/V energy [0.61  0.275 0.958]

```