OUTPUT of run 11 of at most 60:
```
=== VALUE-CHANNEL COORDINATE-CHANGE HYPOTHESIS ===
This is a tangent-space decomposition, not a claim of exact finite equivalence.
Raw metric: ordinary parameter Frobenius inner product.
Balanced metric: O and V terms divided by their midpoint squared norms.
 L gauge_raw% gauge_balanced% controls_balanced%[min,median,max] operator_check
 0     5.4155          7.5325 [ 11.3020,  11.5385,  11.7957] 3.701e-16
 1     4.3212          5.0005 [  9.3384,   9.4728,   9.7819] 3.609e-16
 2     3.0319          5.9264 [ 10.8103,  11.1056,  11.3725] 3.637e-16
 3     3.0179          3.0834 [  8.3359,   8.5767,   8.6647] 3.633e-16
 4     5.8985          6.1760 [  9.4910,   9.8799,  10.2664] 3.585e-16
 5     4.0421          6.5368 [ 10.7496,  10.9844,  11.2490] 3.551e-16
 6     5.1205          7.4435 [ 11.8406,  12.0209,  12.1832] 3.681e-16
 7     2.6166          6.2966 [ 11.2029,  11.3970,  11.6313] 3.674e-16
 8     6.1184          7.6329 [ 10.9405,  11.1479,  11.5026] 3.695e-16
 9     3.5032          7.5386 [ 12.1298,  12.3395,  12.5642] 3.619e-16
10     6.0018          8.3513 [ 12.3374,  12.7119,  12.9865] 3.479e-16
11     2.4024          6.8163 [ 12.6024,  12.7996,  13.1363] 3.645e-16
12     3.7377          5.6593 [ 11.3754,  11.5468,  11.7109] 3.338e-16
13     3.0893          4.0893 [ 10.2708,  10.4014,  10.6236] 3.615e-16
14     3.3550          5.9412 [ 12.3784,  12.6185,  12.8026] 3.609e-16
15     2.7243          6.7330 [ 11.8162,  12.0607,  12.2173] 3.513e-16
16     2.3714          2.7846 [  9.1106,   9.2559,   9.4248] 3.485e-16
17     3.5041          5.8571 [ 10.9484,  11.0917,  11.3795] 3.675e-16

=== SUMMARY ===
Parameter-energy-weighted raw gauge fraction: 0.03921476576056707
Median balanced gauge fraction: 0.06236308099103146
Maximum balanced gauge fraction: 0.0835126222728254
Layers with more than half the balanced difference in gauge directions: []

=== LARGEST GAUGE FRACTIONS ===
L10: balanced=0.083513, control_median=0.127119, actual/control=0.6570
L08: balanced=0.076329, control_median=0.111479, actual/control=0.6847
L09: balanced=0.075386, control_median=0.123395, actual/control=0.6109
L00: balanced=0.075325, control_median=0.115385, actual/control=0.6528
L06: balanced=0.074435, control_median=0.120209, actual/control=0.6192
L11: balanced=0.068163, control_median=0.127996, actual/control=0.5325
L15: balanced=0.067330, control_median=0.120607, actual/control=0.5583
L05: balanced=0.065368, control_median=0.109844, actual/control=0.5951

Maximum product-difference preservation error: 3.700601249794007e-16
Maximum projection orthogonality error: 2.2996366457253042e-17
Maximum projection energy-accounting error: 2.4642119541838395e-17
Elapsed seconds: 2.55

Interpretation limits:
- A large gauge fraction would explain parameter movement without changing
  the composed value/output operator to first order.
- A small fraction rejects coordinate change as the dominant explanation
  for these O/V differences, but does not establish behavioral importance.
- Q/K, MLP, and normalization-parameter changes are outside this test.
- The projection is only a decomposition of existing weight differences;
  no checkpoint was changed and no model input was evaluated.

```