OUTPUT of run 10 of at most 60:
```
=== NEW HYPOTHESIS: SHARED-VALUE CHANGE VERSUS HEAD-SPECIFIC REWRITING ===
Exact identity: delta(O_h V) = delta(O_h) V_mid + O_mid,h delta(V).
Head contrasts are linear combinations of WEIGHT-DERIVED operators.
No attention patterns, input vectors or nonlinear layers are evaluated.
All contribution shares are signed allocations of coefficient-difference energy.

=== ATTRIBUTION OF COMMON AND CONTRAST MODES ===
layer scaled mode total_delta_energy% relative_delta O_share% V_share% O_V_cos head_coefficients
    1 False  common     46.677 0.013891    73.663    26.337 +0.11302 [0.5, 0.5, 0.5, 0.5]
    1 False  leading    47.437 0.013856    73.407    26.593 +0.11586 [0.4824, 0.6271, 0.4471, 0.4173]
    1 False  H2-H3      17.363 0.009746    63.866    36.134 +0.09124 [0.0, 0.0, 0.7071, -0.7071]
    1 True   common     55.325 0.010937    35.849    64.151 +0.15724 [0.5, 0.5, 0.5, 0.5]
    1 True   leading    56.394 0.010862    36.082    63.918 +0.15247 [0.3865, 0.5874, 0.5444, 0.4574]
    1 True   H2-H3      18.014 0.007127    43.864    56.136 +0.14072 [0.0, 0.0, 0.7071, -0.7071]
    4 False  common     60.805 0.020862    85.333    14.667 +0.16885 [0.5, 0.5, 0.5, 0.5]
    4 False  leading    61.137 0.019936    84.623    15.377 +0.16384 [0.4693, 0.4568, 0.4981, 0.5684]
    4 False  H2-H3      13.654 0.008530    46.261    53.739 +0.06157 [0.0, 0.0, 0.7071, -0.7071]
    4 True   common     72.173 0.034665    87.290    12.710 +0.28979 [0.5, 0.5, 0.5, 0.5]
    4 True   leading    72.922 0.033149    87.009    12.991 +0.29585 [0.4355, 0.4538, 0.5647, 0.5343]
    4 True   H2-H3       8.486 0.008924    69.018    30.982 -0.09329 [0.0, 0.0, 0.7071, -0.7071]
    8 False  common     52.398 0.023750    88.233    11.767 +0.11135 [0.5, 0.5, 0.5, 0.5]
    8 False  leading    52.580 0.024116    88.668    11.332 +0.11077 [0.4303, 0.5392, 0.5104, 0.5134]
    8 False  H2-H3      11.538 0.007872    32.050    67.950 +0.04118 [0.0, 0.0, 0.7071, -0.7071]
    8 True   common     48.581 0.024871    80.912    19.088 +0.04857 [0.5, 0.5, 0.5, 0.5]
    8 True   leading    54.990 0.016078    53.400    46.600 +0.10024 [0.8784, 0.3559, 0.2617, 0.1825]
    8 True   H2-H3       5.471 0.009529    50.693    49.307 +0.04741 [0.0, 0.0, 0.7071, -0.7071]
   11 False  common     35.385 0.026559    82.221    17.779 +0.07595 [0.5, 0.5, 0.5, 0.5]
   11 False  leading    36.977 0.012375    63.909    36.091 +0.10547 [0.4608, 0.4408, 0.7649, 0.0905]
   11 False  H2-H3      31.572 0.006538    12.984    87.016 +0.06141 [0.0, 0.0, 0.7071, -0.7071]
   11 True   common     29.372 0.031958    95.658     4.342 +0.11163 [0.5, 0.5, 0.5, 0.5]
   11 True   leading    54.502 0.008173    14.726    85.274 +0.20483 [0.0842, 0.0861, 0.8112, -0.5723]
   11 True   H2-H3      53.380 0.007936    11.631    88.369 +0.13950 [0.0, 0.0, 0.7071, -0.7071]
   12 False  common     49.334 0.014559    55.586    44.414 +0.10334 [0.5, 0.5, 0.5, 0.5]
   12 False  leading    50.855 0.016153    55.911    44.089 +0.10016 [0.5589, 0.477, 0.2951, 0.6108]
   12 False  H2-H3      23.259 0.009976    45.837    54.163 +0.05988 [0.0, 0.0, 0.7071, -0.7071]
   12 True   common     57.079 0.013384    58.182    41.818 +0.36748 [0.5, 0.5, 0.5, 0.5]
   12 True   leading    61.042 0.013063    56.178    43.822 +0.37191 [0.3266, 0.7106, 0.4494, 0.4317]
   12 True   H2-H3      16.239 0.010533    68.928    31.072 +0.12631 [0.0, 0.0, 0.7071, -0.7071]
   15 False  common     52.055 0.025416    66.003    33.997 +0.08318 [0.5, 0.5, 0.5, 0.5]
   15 False  leading    54.185 0.027864    63.791    36.209 +0.08605 [0.2984, 0.6532, 0.5251, 0.4567]
   15 False  H2-H3       8.616 0.008429    33.836    66.164 +0.05467 [0.0, 0.0, 0.7071, -0.7071]
   15 True   common     36.629 0.031948    88.770    11.230 +0.16832 [0.5, 0.5, 0.5, 0.5]
   15 True   leading    52.502 0.016934    27.732    72.268 +0.21600 [0.3468, -0.4697, 0.5748, 0.5734]
   15 True   H2-H3       6.698 0.009538    51.217    48.783 +0.06622 [0.0, 0.0, 0.7071, -0.7071]

=== WHICH PAIRS ARE OPPOSED, AND WHERE? ===
All entries are Frobenius cosines of weight matrices or their products.
layer scaled heads O_mid_cos baseline_OV_cos deltaO_Vmid_cos Omid_deltaV_cos total_deltaOV_cos
    1 False  H2/H3 +0.054754 +0.016971 +0.308606 +0.129537 +0.252502
    1 True   H2/H3 +0.184767 +0.040006 +0.187056 +0.427106 +0.332109
    4 False  H2/H3 -0.025257 +0.025053 +0.668358 +0.035541 +0.503481
    4 False  H0/H1 +0.115640 +0.119409 +0.594469 +0.154016 +0.525947
    4 False  H0/H2 -0.244767 -0.248885 +0.615750 -0.221348 +0.451320
    4 True   H2/H3 +0.031458 +0.004133 +0.703635 +0.196010 +0.699029
    4 True   H0/H1 +0.100843 +0.012970 +0.616995 +0.180138 +0.587855
    4 True   H0/H2 -0.167606 -0.331923 +0.769341 +0.008091 +0.685667
    8 False  H2/H3 -0.173114 -0.177917 +0.768251 -0.132209 +0.499422
    8 True   H2/H3 -0.072136 -0.110627 +0.789966 -0.052611 +0.650230
   11 False  H2/H3 -0.931019 -0.945435 +0.737745 -0.832631 -0.098322
   11 True   H2/H3 -0.987387 -0.977639 +0.668752 -0.986496 -0.420260
   12 False  H2/H3 +0.153452 +0.013245 +0.134179 +0.061919 +0.111339
   12 True   H2/H3 +0.469936 +0.399625 +0.169144 +0.356060 +0.304820
   15 False  H2/H3 +0.222492 +0.214665 +0.762623 +0.391470 +0.613627
   15 False  H1/H2 -0.435035 -0.456087 +0.804232 +0.056959 +0.381249
   15 False  H1/H3 -0.517571 -0.543498 +0.760841 -0.113965 +0.287477
   15 True   H2/H3 +0.675083 +0.143000 +0.715404 +0.681943 +0.724833
   15 True   H1/H2 -0.806464 -0.407427 +0.718896 -0.791466 -0.177501
   15 True   H1/H3 -0.863876 -0.545318 +0.687769 -0.840565 -0.195884

=== SINGULAR-FACTOR DECOMPOSITION OF THE SHARED VALUE CHANGE ===
For deltaV=U diag(s) R.T, O_mid,h U diag(s) describes its transport
through each head's output weights. These are products of weight factors,
not input vectors passed through a model.
Orthogonality of R makes the per-mode squared operator energies additive.

L11, scaled=False:
Top 8 modes' share of VALUE-SIDE H2-H3 contrast energy: 0.3761641296071301
Additive energy identity relative error: 1.130807271582656e-15
singular_index singular_value contrast_energy_share% head2_head3_factor_cos common_to_contrast_energy_ratio
             0 0.0334855      9.48628 -0.319519 0.520493
             1 0.0271754      6.95027 -0.913129 0.046240
             2 0.0217175      4.68327 -0.817170 0.102318
             3 0.0214839      4.33023 -0.887245 0.059786
             4 0.0191936      3.63731 -0.793327 0.120426
             5 0.0178558      3.07038 -0.932847 0.036559
             7 0.0157212      2.80342 -0.952956 0.024693
             6 0.0162093      2.65525 -0.934562 0.034231

L11, scaled=True:
Top 8 modes' share of VALUE-SIDE H2-H3 contrast energy: 0.5383339206787116
Additive energy identity relative error: 5.335171451816395e-16
singular_index singular_value contrast_energy_share% head2_head3_factor_cos common_to_contrast_energy_ratio
             0 0.328708     12.88109 -0.981984 0.009283
             2 0.257764      8.85490 -0.988505 0.006265
             3 0.244653      7.39000 -0.987567 0.006332
             1 0.297589      6.25902 -0.973815 0.013796
             4 0.235671      5.93081 -0.988904 0.005869
             6 0.1953      5.05056 -0.988241 0.006478
             5 0.207501      3.88512 -0.988788 0.005763
             7 0.194915      3.58188 -0.991169 0.004438

L15, scaled=True:
Top 8 modes' share of VALUE-SIDE H2-H3 contrast energy: 0.5479982891338121
Additive energy identity relative error: 8.93898974659446e-16
singular_index singular_value contrast_energy_share% head2_head3_factor_cos common_to_contrast_energy_ratio
             0 1.32477     10.85707 +0.581222 3.726059
             2 1.15791      9.57719 +0.717082 6.005601
             1 1.23904      9.15971 +0.731351 6.281976
             3 0.99192      6.63265 +0.673399 4.978469
             4 0.919219      5.55408 +0.687914 5.345877
             5 0.856137      4.61744 +0.664307 4.909430
             7 0.781085      4.33433 +0.636613 4.440985
             6 0.812256      4.06736 +0.682482 5.272532

Interpretation boundary:
This can locate the origin of opposing coefficient changes.
It cannot identify the transported content or the resulting behaviour.

```