=== TEST: SHARED RESIDUAL-OUTPUT DIRECTION ===
All calculations are contractions/eigendecompositions of weight coefficients.
No input vectors, activations, attention scores, or forward passes.
Learned output norm diagonals put coefficient numerators in residual coordinates.
State-dependent normalization denominators remain excluded.
Attention: value-output coefficient maps, not routing changes.
MLP: exact even-component coefficients, not the complete nonlinear block.
Midpoint controls use the midpoint of coefficient operators, not midpoint weights.
Each block has equal weight in aggregate direction tests.

layer  0: attention top-axis energy delta=0.5815, midpoint=0.5093; MLP delta=0.7457, midpoint=0.5713
layer  1: attention top-axis energy delta=0.6270, midpoint=0.7839; MLP delta=0.7341, midpoint=0.4983
layer  2: attention top-axis energy delta=0.7181, midpoint=0.5555; MLP delta=0.6217, midpoint=0.4930
layer  3: attention top-axis energy delta=0.6712, midpoint=0.4282; MLP delta=0.4946, midpoint=0.3335
layer  4: attention top-axis energy delta=0.6151, midpoint=0.5411; MLP delta=0.7765, midpoint=0.7549
layer  5: attention top-axis energy delta=0.6014, midpoint=0.7695; MLP delta=0.6844, midpoint=0.6871
layer  6: attention top-axis energy delta=0.5355, midpoint=0.4596; MLP delta=0.7657, midpoint=0.9206
layer  7: attention top-axis energy delta=0.6227, midpoint=0.5690; MLP delta=0.6130, midpoint=0.8792
layer  8: attention top-axis energy delta=0.4862, midpoint=0.5844; MLP delta=0.5455, midpoint=0.5794
layer  9: attention top-axis energy delta=0.3876, midpoint=0.2589; MLP delta=0.2573, midpoint=0.3102
layer 10: attention top-axis energy delta=0.1421, midpoint=0.0584; MLP delta=0.1952, midpoint=0.2668
layer 11: attention top-axis energy delta=0.0624, midpoint=0.0792; MLP delta=0.0852, midpoint=0.0582
layer 12: attention top-axis energy delta=0.0835, midpoint=0.0422; MLP delta=0.0705, midpoint=0.0408
layer 13: attention top-axis energy delta=0.0785, midpoint=0.0505; MLP delta=0.0733, midpoint=0.0315
layer 14: attention top-axis energy delta=0.0740, midpoint=0.0846; MLP delta=0.0644, midpoint=0.0306
layer 15: attention top-axis energy delta=0.0793, midpoint=0.0368; MLP delta=0.0604, midpoint=0.0506
layer 16: attention top-axis energy delta=0.1361, midpoint=0.0486; MLP delta=0.0714, midpoint=0.0693
layer 17: attention top-axis energy delta=0.0608, midpoint=0.0490; MLP delta=0.0932, midpoint=0.0807

=== AGGREGATE SHARED-DIRECTION CONCENTRATION ===
group       type      top1_share top5_share effective_rank
attention   delta       0.213307   0.422400         12.787
attention   mid         0.190223   0.389190         15.220
mlp         delta       0.253831   0.450998         10.799
mlp         mid         0.271330   0.428918         10.529
all         delta       0.229806   0.429983         11.902
all         mid         0.227429   0.403940         12.901

=== PAIRWISE LEADING-DIRECTION AGREEMENT ===
Squared cosine ignores arbitrary eigenvector sign.
Isotropic-reference squared cosine is 1/640 = 0.0015625 (reference only, not a statistical null model).
Top-5 overlap is ||U_i.T U_j||_F^2 / 5.
Its isotropic reference is 5/640 = 0.0078125
group       type      mean_top1_cos2 median_top1_cos2 mean_top5_overlap
attention   delta            0.211599          0.039886          0.160779
attention   mid              0.178611          0.015224          0.169601
mlp         delta            0.270603          0.087807          0.199228
mlp         mid              0.507098          0.788701          0.232333
all         delta            0.250141          0.076786          0.182604
all         mid              0.327786          0.045873          0.200089

=== ATTENTION / MLP AGREEMENT WITHIN EACH LAYER ===
layer delta_top1_cos2 midpoint_top1_cos2 delta_top5_overlap midpoint_top5_overlap
    0         0.973729            0.953933           0.351118              0.368947
    1         0.769307            0.772721           0.261721              0.436290
    2         0.987472            0.982237           0.308505              0.543925
    3         0.031704            0.854605           0.429344              0.533868
    4         0.987816            0.639623           0.427289              0.402293
    5         0.803736            0.557837           0.642592              0.745851
    6         0.962197            0.844191           0.505898              0.675901
    7         0.974766            0.964467           0.551635              0.670316
    8         0.961475            0.991012           0.557773              0.527668
    9         0.952298            0.980548           0.456064              0.482687
   10         0.328786            0.395961           0.247327              0.183655
   11         0.032082            0.000093           0.092613              0.037359
   12         0.102216            0.011114           0.168381              0.039312
   13         0.149649            0.013515           0.146231              0.155687
   14         0.292515            0.006181           0.162193              0.153311
   15         0.043305            0.021087           0.119976              0.075862
   16         0.285742            0.748517           0.277838              0.162956
   17         0.185629            0.004556           0.137061              0.030228

=== AGGREGATE DIRECTION CONTROLS ===
delta aggregate attention/MLP leading-axis squared cosine: 0.7553873229275164
mid aggregate attention/MLP leading-axis squared cosine: 0.7307401198756216
All-block difference axis versus midpoint axis squared cosine: 0.9739891218396246
Smallest eigenvalue/trace across individual Gram matrices: -4.224285176466168e-20

Interpretation:
A shared change axis should concentrate difference energy across blocks,
not merely reproduce directional concentration in the midpoint control.
Even a positive result would identify coefficient geometry,
not whether that direction means agreement, correctness, or another feature.
