OUTPUT of run 8 of at most 60:
```
=== ATTENTION VALUE-BASIS SYMMETRY TEST ===
Projection uses the midpoint weight geometry and one shared basis change across all heads.
layer | symmetry_fraction residual_fraction | relative_OV_change | orthogonality_error product_preservation_error
 0 | 0.0559273 0.9440727 | 0.0088156 | +0.000e+00 3.653e-16
 1 | 0.0442651 0.9557349 | 0.0120759 | +2.005e-18 3.517e-16
 2 | 0.0307051 0.9692949 | 0.0100533 | +5.856e-18 3.609e-16
 3 | 0.0308869 0.9691131 | 0.0130603 | +1.382e-18 3.648e-16
 4 | 0.0451923 0.9548077 | 0.0129684 | -3.817e-18 3.626e-16
 5 | 0.0392752 0.9607248 | 0.0108015 | +3.162e-18 3.562e-16
 6 | 0.0469774 0.9530226 | 0.0106551 | -3.175e-18 3.633e-16
 7 | 0.0275756 0.9724244 | 0.0098150 | -7.913e-18 3.692e-16
 8 | 0.0532892 0.9467108 | 0.0111540 | -1.360e-17 3.691e-16
 9 | 0.0396441 0.9603559 | 0.0107940 | -1.143e-17 3.473e-16
10 | 0.0658550 0.9341450 | 0.0098291 | +1.069e-18 3.520e-16
11 | 0.0246849 0.9753151 | 0.0093692 | -5.846e-18 3.650e-16
12 | 0.0392882 0.9607118 | 0.0109725 | -1.396e-17 3.360e-16
13 | 0.0321022 0.9678978 | 0.0118617 | -3.458e-18 3.584e-16
14 | 0.0348133 0.9651867 | 0.0092559 | -1.466e-17 3.614e-16
15 | 0.0263416 0.9736584 | 0.0114059 | -1.686e-18 3.521e-16
16 | 0.0230782 0.9769218 | 0.0146089 | -7.945e-18 3.456e-16
17 | 0.0348963 0.9651037 | 0.0095346 | +7.103e-18 3.681e-16

Global attention symmetry fraction: 0.038674528809723066
Nominal symmetry-dimension / parameter-dimension ratio: 0.08
That dimension ratio is a geometric reference, not a calibrated null model.
Maximum symmetry-product null error: 1.2112364872786041e-16
Smallest Sylvester denominator: 0.23780194008131533

=== MLP UP/DOWN SCALING-SYMMETRY TEST ===
layer | fraction_of_up_down_change fraction_of_all_MLP_change | median_unit_fraction max_unit_fraction | relative_dyad_change
 0 | 0.0004835 0.0003170 | 0.0002074 0.0060731 | 0.0119530
 1 | 0.0006427 0.0004175 | 0.0002680 0.0094075 | 0.0174346
 2 | 0.0006574 0.0004233 | 0.0002704 0.0206299 | 0.0144619
 3 | 0.0006703 0.0004258 | 0.0002865 0.0222436 | 0.0164541
 4 | 0.0007930 0.0005091 | 0.0003457 0.0132095 | 0.0187060
 5 | 0.0005307 0.0003405 | 0.0002390 0.0075835 | 0.0115810
 6 | 0.0006685 0.0004218 | 0.0002582 0.0148515 | 0.0151607
 7 | 0.0006244 0.0003967 | 0.0002739 0.0106659 | 0.0137141
 8 | 0.0007276 0.0004622 | 0.0003405 0.0119868 | 0.0168530
 9 | 0.0006229 0.0004014 | 0.0002698 0.0075040 | 0.0130685
10 | 0.0007198 0.0004604 | 0.0003260 0.0102098 | 0.0169590
11 | 0.0006583 0.0004149 | 0.0002874 0.0178435 | 0.0129391
12 | 0.0004937 0.0003173 | 0.0002131 0.0100857 | 0.0125103
13 | 0.0005832 0.0003798 | 0.0002599 0.0083867 | 0.0174357
14 | 0.0006312 0.0004100 | 0.0002809 0.0180886 | 0.0190019
15 | 0.0005316 0.0003488 | 0.0002179 0.0086489 | 0.0166026
16 | 0.0005400 0.0003534 | 0.0002336 0.0103010 | 0.0152867
17 | 0.0006730 0.0004350 | 0.0002884 0.0176511 | 0.0152205

Global MLP symmetry fraction of up/down changes: 0.0006222095492264426
Global MLP symmetry fraction including gate changes: 0.0004006404449740056
Scalar-symmetry dimension / up-down parameter dimension: 0.00078125

=== UNITS WITH LARGEST FRACTION OF UP/DOWN CHANGE IN THE SCALING DIRECTION ===
layer unit | symmetry_fraction pair_change_norm symmetry_change_norm alpha
 3  385 | 0.0222436 0.007705263 0.001149184 -0.001271515
 2 1050 | 0.0206299 0.007395396 0.00106221 +0.001070003
14 1867 | 0.0180886 0.007252241 0.0009753808 -0.001405518
11 1428 | 0.0178435 0.008190017 0.00109402 -0.0008981984
17 1650 | 0.0176511 0.009871587 0.001311514 +0.0009605579
17 1816 | 0.0152017 0.007988512 0.0009849435 +0.0008060558
 6    2 | 0.0148515 0.007794881 0.0009499364 -0.001115604
 3  108 | 0.0132893 0.008678928 0.001000499 -0.0009780956
 4 1491 | 0.0132095 0.008350123 0.0009597 +0.000882744
 3 1047 | 0.0123277 0.007162634 0.0007952669 +0.001016804
 8  815 | 0.0119868 0.00721614 0.000790054 -0.0009076089
 2  743 | 0.0111348 0.006875998 0.0007255657 +0.0007013957
17 1588 | 0.0108457 0.007927456 0.0008255869 +0.0007153662
 7  764 | 0.0106659 0.007213475 0.0007449775 +0.0006778031
17    6 | 0.0106633 0.008451079 0.0008726839 +0.0008057426
16  509 | 0.0103010 0.009202536 0.0009340017 -0.0008579445
10 1947 | 0.0102098 0.008025923 0.0008109692 -0.0007269965
 8 1085 | 0.0101139 0.00843516 0.0008483052 -0.0006736119
12 1795 | 0.0100857 0.008047483 0.000808189 -0.0007710719
 8 1460 | 0.0100119 0.007351245 0.0007355609 +0.0006441988

=== PREVIOUS MLP CANDIDATES: SYMMETRY FRACTIONS ===
layer= 2 unit=1831 up_down_symmetry_fraction=0.0019599
layer= 3 unit=  82 up_down_symmetry_fraction=0.0040416
layer= 3 unit= 226 up_down_symmetry_fraction=0.0010866
layer= 3 unit= 986 up_down_symmetry_fraction=0.0020946
layer= 3 unit=1414 up_down_symmetry_fraction=0.0020406
layer=10 unit=1363 up_down_symmetry_fraction=0.0006392
layer=12 unit= 259 up_down_symmetry_fraction=0.0004538
layer=14 unit= 641 up_down_symmetry_fraction=0.0010211
layer=16 unit= 893 up_down_symmetry_fraction=0.0006038

Limitations:
- These are midpoint tangent-space diagnostics, not a complete classification of finite equivalences.
- The attention symmetry preserves OV maps, not changes in query/key routing.
- The MLP symmetry holds with its gate fixed; changing gates introduces additional interactions.
- No transformed checkpoint, model execution, nonlinear evaluation, or training was performed.
- A non-symmetry change still need not matter on the unknown training or evaluation inputs.

```