OUTPUT of run 26 of at most 60:
```
=== EXACT SHARED-VALUE COORDINATE SYMMETRY ===
For any invertible S: (O_h @ inv(S)) @ (S @ V) = O_h @ V.
Because the same S is used for the shared V and all four O heads,
this reparameterisation leaves attention's value/output computation
unchanged for every possible attention pattern. No pattern is evaluated.
S is obtained by an SVD-based map between parameter row spaces.
This is weight alignment, not model training or optimisation.

=== DOES THE OBSERVED O CHANGE COMPENSATE THE VALUE-BASIS CHANGE? ===
L method cond(S) | V residual/original | O residual/original | task-O residual/original | observed/gauge O-change cosine
Ratios near zero would indicate strong removal by coordinate alignment.
Ratios >=1 mean alignment does not explain away the corresponding change.
 0 row-space    1.045 | 0.725 | 1.457 | 1.448 | -0.091
 1 row-space    1.035 | 0.738 | 1.188 | 1.209 | -0.159
 2 row-space    1.028 | 0.724 | 1.266 | 1.236 | -0.150
 3 row-space    1.027 | 0.735 | 1.142 | 1.117 | -0.151
 4 row-space    1.030 | 0.732 | 1.163 | 1.166 | -0.151
 5 row-space    1.038 | 0.739 | 1.316 | 1.298 | -0.129
 6 row-space    1.033 | 0.763 | 1.268 | 1.240 | -0.105
 7 row-space    1.038 | 0.732 | 1.304 | 1.296 | -0.117
 8 row-space    1.028 | 0.738 | 1.212 | 1.210 | -0.116
 9 row-space    1.029 | 0.765 | 1.301 | 1.269 | -0.088
10 row-space    1.031 | 0.751 | 1.373 | 1.354 | -0.133
11 row-space    1.030 | 0.785 | 1.285 | 1.337 | -0.088
12 row-space    1.030 | 0.743 | 1.359 | 1.395 | -0.118
13 row-space    1.028 | 0.793 | 1.227 | 1.230 | -0.138
14 row-space    1.030 | 0.809 | 1.354 | 1.238 | -0.103
15 row-space    1.025 | 0.756 | 1.324 | 1.258 | -0.107
16 row-space    1.027 | 0.797 | 1.198 | 1.127 | -0.130
17 row-space    1.022 | 0.785 | 1.200 | 1.104 | -0.102

Maximum relative gauge-identity discrepancy: 7.134750186547575e-16

=== TOP FIVE HEADS PER DOMAIN USING GAUGE-INVARIANT OV CHANGES ===
Ranking uses minimum raw/diagonal matched-vocabulary enrichment.
digits
 L17H3: OV enrichment=16.27/18.97; OV task fraction=26.00%/27.59%; aligned/original task-O change=1.027/1.026
 L16H3: OV enrichment=10.37/9.96; OV task fraction=15.86%/12.25%; aligned/original task-O change=1.082/1.066
 L16H2: OV enrichment=9.39/10.40; OV task fraction=13.38%/11.75%; aligned/original task-O change=1.131/1.111
 L16H1: OV enrichment=8.81/8.75; OV task fraction=13.09%/10.58%; aligned/original task-O change=1.082/1.050
 L16H0: OV enrichment=7.17/6.71; OV task fraction=11.11%/8.55%; aligned/original task-O change=1.088/1.055
colors
 L17H2: OV enrichment=8.10/10.53; OV task fraction=10.94%/11.87%; aligned/original task-O change=1.123/1.128
 L17H0: OV enrichment=3.84/5.59; OV task fraction=4.68%/5.63%; aligned/original task-O change=1.079/1.080
 L17H1: OV enrichment=3.39/5.10; OV task fraction=4.33%/5.37%; aligned/original task-O change=1.151/1.152
 L12H2: OV enrichment=2.18/4.15; OV task fraction=2.61%/3.52%; aligned/original task-O change=1.462/1.283
 L16H2: OV enrichment=2.39/2.11; OV task fraction=2.55%/1.91%; aligned/original task-O change=1.175/1.115
regions
 L17H2: OV enrichment=3.52/3.35; OV task fraction=3.68%/2.86%; aligned/original task-O change=1.131/1.143
 L17H1: OV enrichment=3.21/3.01; OV task fraction=3.34%/2.83%; aligned/original task-O change=1.170/1.170
 L17H0: OV enrichment=2.55/3.18; OV task fraction=2.44%/2.78%; aligned/original task-O change=1.142/1.144
 L12H2: OV enrichment=1.93/4.92; OV task fraction=1.72%/2.82%; aligned/original task-O change=1.294/1.277
 L15H3: OV enrichment=1.82/3.16; OV task fraction=1.50%/1.59%; aligned/original task-O change=1.313/1.321
cities
 L17H0: OV enrichment=1.65/2.02; OV task fraction=3.28%/3.29%; aligned/original task-O change=1.244/1.232
 L15H3: OV enrichment=1.48/2.32; OV task fraction=2.84%/2.91%; aligned/original task-O change=1.411/1.407
 L17H2: OV enrichment=1.46/1.56; OV task fraction=3.19%/2.91%; aligned/original task-O change=1.161/1.163
 L17H1: OV enrichment=1.39/1.67; OV task fraction=3.05%/2.96%; aligned/original task-O change=1.157/1.148
 L13H3: OV enrichment=1.35/1.98; OV task fraction=2.53%/2.65%; aligned/original task-O change=1.352/1.542
languages
 L17H0: OV enrichment=1.56/1.70; OV task fraction=2.45%/2.37%; aligned/original task-O change=1.294/1.298
 L11H3: OV enrichment=1.52/3.06; OV task fraction=1.90%/2.68%; aligned/original task-O change=1.391/1.606
 L17H1: OV enrichment=1.51/1.85; OV task fraction=2.33%/2.34%; aligned/original task-O change=1.204/1.159
 L17H3: OV enrichment=1.39/1.73; OV task fraction=1.99%/2.10%; aligned/original task-O change=1.064/1.052
 L17H2: OV enrichment=1.38/1.80; OV task fraction=2.30%/2.52%; aligned/original task-O change=1.214/1.217

=== L17 HEAD SHARES OF GAUGE-INVARIANT OV CHANGE BY DOMAIN ===
These are squared weight-operator shares, not attention or behavioural shares.
digits     raw=[0.147 0.186 0.109 0.558] diag=[0.137 0.191 0.098 0.574]
colors     raw=[0.221 0.234 0.458 0.087] diag=[0.227 0.26  0.441 0.072]
regions    raw=[0.229 0.361 0.307 0.102] diag=[0.29  0.354 0.274 0.082]
cities     raw=[0.27  0.288 0.233 0.208] diag=[0.284 0.306 0.231 0.18 ]
languages  raw=[0.274 0.3   0.229 0.197] diag=[0.26  0.308 0.254 0.178]

This tests an exactly function-preserving coordinate explanation.
Persistent OV structure still does not establish contextual routing,
nonlinear downstream effects, or causal behavioural importance.

```