=== CROSS-HEAD COMPENSATION TEST ===
Common fraction = ||sum_h delta M_h||^2 / (H * sum_h ||delta M_h||^2).
The remainder is the orthogonal head-contrast component.
Uncorrelated head-map changes have reference common fraction 1/H = 0.25
This is a geometric reference, not a statistical null model.

=== ALL LAYERS ===
layer | gain-weighted common contrast baseline_common | raw common baseline_common | relative_summed_map_change | min/max head-change cosine
 0 | 0.513980 0.486020 0.352982 | 0.412532 0.271377 | 0.011627 | +0.22055 +0.48812
 1 | 0.634520 0.365480 0.404187 | 0.488074 0.336924 | 0.013380 | +0.42376 +0.62305
 2 | 0.517181 0.482819 0.174002 | 0.412751 0.161632 | 0.023808 | +0.19331 +0.48769
 3 | 0.557341 0.442659 0.222806 | 0.484895 0.184016 | 0.029519 | +0.32717 +0.59570
 4 | 0.708812 0.291188 0.212402 | 0.602750 0.257125 | 0.036348 | +0.51948 +0.73887
 5 | 0.630847 0.369153 0.415638 | 0.478771 0.278878 | 0.011968 | +0.36446 +0.67216
 6 | 0.582893 0.417107 0.095121 | 0.465966 0.125170 | 0.036135 | +0.22154 +0.65352
 7 | 0.528697 0.471303 0.102364 | 0.438850 0.073148 | 0.026045 | +0.20438 +0.56831
 8 | 0.522167 0.477833 0.169117 | 0.527236 0.130255 | 0.024230 | +0.17148 +0.67274
 9 | 0.458138 0.541862 0.080555 | 0.374620 0.063207 | 0.031367 | +0.09913 +0.61049
10 | 0.509564 0.490436 0.263656 | 0.479459 0.285627 | 0.013830 | +0.25925 +0.44144
11 | 0.321354 0.678646 0.029584 | 0.344945 0.047902 | 0.032547 | -0.37123 +0.41854
12 | 0.563155 0.436845 0.420229 | 0.481898 0.278575 | 0.013455 | +0.15130 +0.58515
13 | 0.437530 0.562470 0.185352 | 0.446901 0.186263 | 0.015689 | +0.09260 +0.36432
14 | 0.372244 0.627756 0.168212 | 0.397093 0.186144 | 0.013802 | +0.11726 +0.22218
15 | 0.394380 0.605620 0.088831 | 0.519433 0.103980 | 0.033695 | -0.14796 +0.67979
16 | 0.604018 0.395982 0.180781 | 0.657793 0.196129 | 0.025375 | +0.41554 +0.57137
17 | 0.378029 0.621971 0.095832 | 0.374914 0.144406 | 0.019020 | +0.01206 +0.32478

=== AGGREGATE COMMON/CONTRAST FRACTIONS ===
raw energy_weighted_common_fraction= 0.4616643115508274 equal_layer_mean_common_fraction= 0.466048955055709
scaled energy_weighted_common_fraction= 0.4566980122568504 equal_layer_mean_common_fraction= 0.5130471224517381

=== STRONGEST GAIN-WEIGHTED HEAD COMPENSATION ===

Layer 11
Head-change correlation matrix:
[[ 1.      0.4185  0.3259  0.1764]
 [ 0.4185  1.      0.2947  0.1736]
 [ 0.3259  0.2947  1.     -0.3712]
 [ 0.1764  0.1736 -0.3712  1.    ]]
Signed contributions to summed-map change: [0.2462 0.2271 0.3189 0.2077]
Leading head-combination coefficients: [ 0.1344  0.1139  0.8183 -0.5471]
Leading combination's change-energy share: 0.5105161391154429

Layer 14
Head-change correlation matrix:
[[1.     0.2222 0.2085 0.1173]
 [0.2222 1.     0.2037 0.1231]
 [0.2085 0.2037 1.     0.1314]
 [0.1173 0.1231 0.1314 1.    ]]
Signed contributions to summed-map change: [0.2252 0.2371 0.2618 0.2759]
Leading head-combination coefficients: [0.3781 0.415  0.5102 0.6515]
Leading combination's change-energy share: 0.3784681470237174

Layer 17
Head-change correlation matrix:
[[1.     0.2251 0.0121 0.2097]
 [0.2251 1.     0.3248 0.1357]
 [0.0121 0.3248 1.     0.1142]
 [0.2097 0.1357 0.1142 1.    ]]
Signed contributions to summed-map change: [0.2497 0.3167 0.2651 0.1684]
Leading head-combination coefficients: [0.3886 0.7065 0.556  0.202 ]
Leading combination's change-energy share: 0.4098286558184592

Layer 15
Head-change correlation matrix:
[[ 1.     -0.0652  0.482   0.6189]
 [-0.0652  1.     -0.1345 -0.148 ]
 [ 0.482  -0.1345  1.      0.6798]
 [ 0.6189 -0.148   0.6798  1.    ]]
Signed contributions to summed-map change: [0.2377 0.1586 0.2968 0.3069]
Leading head-combination coefficients: [ 0.4092 -0.349   0.587   0.6051]
Leading combination's change-energy share: 0.5062270736953249

Layer 13
Head-change correlation matrix:
[[1.     0.2845 0.284  0.3635]
 [0.2845 1.     0.3643 0.0926]
 [0.284  0.3643 1.     0.2359]
 [0.3635 0.0926 0.2359 1.    ]]
Signed contributions to summed-map change: [0.2639 0.1807 0.1904 0.365 ]
Leading head-combination coefficients: [0.4313 0.177  0.2405 0.8514]
Leading combination's change-energy share: 0.5171165592028656

Layer 9
Head-change correlation matrix:
[[1.     0.2356 0.3572 0.3405]
 [0.2356 1.     0.0991 0.1105]
 [0.3572 0.0991 1.     0.6105]
 [0.3405 0.1105 0.6105 1.    ]]
Signed contributions to summed-map change: [0.245  0.2394 0.2695 0.2461]
Leading head-combination coefficients: [0.4843 0.4317 0.5677 0.5067]
Leading combination's change-energy share: 0.4600703116099041

=== PREVIOUS ATTENTION CANDIDATE LAYERS ===
Signed shares below concern the summed map only, not actual head importance.
layer 10 gain_weighted_shares= [0.2728 0.2116 0.2489 0.2668] raw_shares= [0.2547 0.203  0.2805 0.2618]
layer 11 gain_weighted_shares= [0.2462 0.2271 0.3189 0.2077] raw_shares= [0.2473 0.2674 0.2761 0.2091]
layer 12 gain_weighted_shares= [0.1819 0.3377 0.2468 0.2337] raw_shares= [0.2582 0.2563 0.2016 0.2839]
layer 15 gain_weighted_shares= [0.2377 0.1586 0.2968 0.3069] raw_shares= [0.2021 0.2801 0.2691 0.2487]
layer 17 gain_weighted_shares= [0.2497 0.3167 0.2651 0.1684] raw_shares= [0.2582 0.3187 0.2396 0.1835]

=== SIGNED IDENTITY-ALIGNMENT CHANGES OF SUMMED VALUE MAPS ===
Positive B-A means greater identity alignment in B, not identified guess copying.
layer= 6 A=+0.08321608 B=+0.08306378 B_minus_A=-0.00015229
layer= 3 A=+0.01068666 B=+0.01062272 B_minus_A=-0.00006394
layer= 9 A=+0.03617857 B=+0.03620663 B_minus_A=+0.00002805
layer= 8 A=-0.00490107 B=-0.00487354 B_minus_A=+0.00002753
layer= 7 A=-0.00486004 B=-0.00483282 B_minus_A=+0.00002722
layer= 4 A=-0.00520134 B=-0.00522674 B_minus_A=-0.00002540
layer=11 A=+0.01855010 B=+0.01857076 B_minus_A=+0.00002066
layer= 5 A=+0.00409030 B=+0.00407116 B_minus_A=-0.00001914
layer=14 A=+0.05068596 B=+0.05066882 B_minus_A=-0.00001715
layer=15 A=+0.05454635 B=+0.05456083 B_minus_A=+0.00001448

Interpretation limits:
- Summed value maps describe the shared-mixture case algebraically; actual heads may attend differently.
- A head-contrast change can have a large effect when head attention patterns differ.
- Query/key routing changes and output RMS denominators are not included in this test.
- Negative signed contributions are matrix cancellation, not opposition to a semantic behavior.
- No attention probabilities, inputs, activations, model execution or training were used.
