=== OUTPUT-MATRIX ROTATION DECOMPOSITION ===
The rotation acts on the FULL attention output matrix before its
post-attention normalisation. It preserves the pre-normalisation norm
for every possible concatenated value vector, without evaluating one.
Head terms are column partitions of that joint rotation; an isolated
head replacement would not inherit the same norm-preservation guarantee.
No attention mixing, hidden-state norm, activation, or model output is computed.
L0: orthogonality error=1.23e-13; rotation/full difference norm=0.570; remainder/full=0.822
L15: orthogonality error=1.25e-13; rotation/full difference norm=0.453; remainder/full=0.892
L16: orthogonality error=1.26e-13; rotation/full difference norm=0.552; remainder/full=0.834
L17: orthogonality error=1.23e-13; rotation/full difference norm=0.544; remainder/full=0.839

=== SIGNED IDENTITY-TRANSFER COEFFICIENTS ===
All changes are B-A. Each domain entry: full / rotation / reverse-origin rotation.
These are weight-product coefficients, NOT predicted token scores.
L H geo | digits | colors | regions
 0 0 raw  | -0.000383/+2.62e-05/+2.8e-05 | -6.18e-06/-3e-05/-2.96e-05 | +2.56e-05/-0.000106/-0.000105
 0 1 raw  | -0.000211/-5.85e-05/-5.39e-05 | -0.000145/+1.07e-05/+1.1e-05 | -0.000491/-0.000118/-0.000116
 0 2 raw  | -0.000174/+3.43e-05/+3.89e-05 | -8.66e-05/+1.34e-05/+1.36e-05 | -0.000457/-5.21e-05/-5.06e-05
 0 3 raw  | -0.000128/-7.4e-05/-6.99e-05 | -0.000256/-5.05e-06/-4.2e-06 | +5.54e-05/+2.63e-05/+2.54e-05
 0 0 diag | -0.117/+0.000667/+0.00145 | -0.121/-0.0373/-0.0372 | -0.00829/-0.0183/-0.0189
 0 1 diag | -0.0435/-0.028/-0.0277 | -0.0313/+0.0114/+0.0113 | -0.115/-0.0424/-0.0423
 0 2 diag | -0.0278/-0.00396/-0.00316 | +0.0265/+0.000112/-0.000291 | +0.0443/-0.0113/-0.0106
 0 3 diag | -0.111/-0.0437/-0.0421 | -0.0665/-0.00462/-0.00433 | +0.0446/-0.0219/-0.0226
15 0 raw  | +0.000118/+3.69e-05/+3.41e-05 | -4.14e-05/-3.13e-05/-3.09e-05 | +0.000179/+2.95e-05/+2.84e-05
15 1 raw  | -0.000131/-8.31e-06/-2.45e-05 | +4.08e-05/+1.33e-05/+1e-05 | +3.68e-06/+9.17e-06/+5.05e-06
15 2 raw  | -0.000202/-3.66e-06/-5.58e-06 | -8.61e-06/-5.07e-05/-5.1e-05 | -3.56e-05/-3.08e-05/-3.04e-05
15 3 raw  | +0.000243/+2.81e-05/+2.16e-05 | +0.000162/+5.25e-05/+5.35e-05 | +0.000214/+6.52e-05/+6.61e-05
15 0 diag | -14.7/-3.66/-3.68 | -5.84/-1.52/-1.53 | +28.7/+6.65/+6.58
15 1 diag | -30.6/-8.15/-8.5 | -8.54/+2.28/+2.24 | +4.99/-2.04/-2.21
15 2 diag | -6.25/+3.19/+3.19 | +2.12/-3.19/-3.19 | +12.1/-2.53/-2.59
15 3 diag | +2.14/+0.499/+0.458 | +11.3/+2.88/+2.91 | +28/+5.17/+5.13
16 0 raw  | +0.000106/+0.000143/+0.000135 | +0.000108/+1.06e-05/+1.33e-05 | +0.000182/+6.67e-06/+6.69e-06
16 1 raw  | -0.000211/-5.59e-05/-5.5e-05 | +0.000128/+7.37e-06/+9.53e-06 | -4.42e-05/-9.79e-06/-8.6e-06
16 2 raw  | -7.51e-05/+0.000121/+0.000137 | +0.000252/+8.78e-05/+8.88e-05 | +0.000273/+7.58e-05/+7.44e-05
16 3 raw  | -7.68e-05/-6.78e-05/-7.66e-05 | +0.00011/-9.18e-05/-9.22e-05 | -0.000246/-1.66e-05/-1.57e-05
16 0 diag | +7.18/+13.2/+13.1 | +11.6/+3.82/+3.98 | +0.407/-0.632/-0.757
16 1 diag | -23/+0.559/+0.519 | +10.4/+0.851/+1.01 | +2.79/+0.205/+0.211
16 2 diag | -4.75/+12.6/+13 | +15.8/+5.14/+5.36 | +1.57/-0.478/-0.498
16 3 diag | -8.75/-5.09/-5.09 | +13.2/+0.628/+0.712 | -3/-0.488/-0.609
17 0 raw  | -0.0003/-7.46e-05/-8.2e-05 | +3.57e-05/-3.67e-06/-3.54e-06 | +0.000162/+0.000101/+0.000104
17 1 raw  | +4.1e-05/-0.000118/-7.8e-05 | -6.13e-06/+0.000123/+0.000132 | +0.000641/+0.000154/+0.00016
17 2 raw  | +8.49e-05/+5.84e-05/+5.34e-05 | +6.5e-05/-8.56e-05/-8.9e-05 | +0.000175/+8.17e-05/+8.13e-05
17 3 raw  | -0.000541/-7.82e-05/-7.98e-05 | -7.8e-05/-1.42e-05/-1.48e-05 | +0.000279/+1.16e-05/+1.12e-05
17 0 diag | +2.22/+2.66/+2.29 | +4.84/-0.585/-0.606 | -0.381/-0.414/-0.353
17 1 diag | +2.49/-6.36/-5.37 | +4/+3.44/+3.54 | +11.9/+1.76/+1.81
17 2 diag | +10.4/+5.28/+5.02 | +11.2/+1.04/+0.979 | +12.3/+3.97/+3.94
17 3 diag | +2.46/-0.0101/-0.125 | +1.34/-0.508/-0.55 | +6.13/+1.64/+1.61

=== TASK-SPECIALISED HEADS AND EARLY ROUTING CANDIDATE ===
L0H3 raw digits: A=+0.0332951, B=+0.0331668; full=-0.00012834 = rotation -7.4009e-05 + other-output -0.00014178 + value/input-diagonal +8.7449e-05
L0H3 raw colors: A=+0.12636, B=+0.126104; full=-0.00025604 = rotation -5.0492e-06 + other-output +2.4554e-05 + value/input-diagonal -0.00027555
L0H3 raw regions: A=+0.139373, B=+0.139428; full=+5.5378e-05 = rotation +2.63e-05 + other-output -4.3764e-05 + value/input-diagonal +7.2842e-05
L0H3 diag digits: A=-2.06254, B=-2.17357; full=-0.11102 = rotation -0.043665 + other-output -0.052318 + value/input-diagonal -0.015041
L0H3 diag colors: A=+3.49554, B=+3.42901; full=-0.066527 = rotation -0.004619 + other-output +0.00021036 + value/input-diagonal -0.062118
L0H3 diag regions: A=+9.81029, B=+9.85484; full=+0.044552 = rotation -0.021888 + other-output -0.0082269 + value/input-diagonal +0.074667
L16H1 raw digits: A=+0.0120616, B=+0.0118505; full=-0.00021104 = rotation -5.5945e-05 + other-output -0.00021833 + value/input-diagonal +6.3233e-05
L16H2 raw digits: A=+0.0912123, B=+0.0911373; full=-7.5077e-05 = rotation +0.00012083 + other-output -8.7224e-05 + value/input-diagonal -0.00010869
L16H3 raw digits: A=-0.0128857, B=-0.0129625; full=-7.6827e-05 = rotation -6.7844e-05 + other-output -2.5033e-05 + value/input-diagonal +1.6051e-05
L16H1 diag digits: A=+241.608, B=+218.617; full=-22.991 = rotation +0.55945 + other-output -22.149 + value/input-diagonal -1.4014
L16H2 diag digits: A=+1604.69, B=+1599.93; full=-4.7544 = rotation +12.571 + other-output -9.0316 + value/input-diagonal -8.2936
L16H3 diag digits: A=+227.03, B=+218.28; full=-8.75 = rotation -5.0891 + other-output -5.2362 + value/input-diagonal +1.5753
L17H1 raw regions: A=+0.193083, B=+0.193724; full=+0.00064141 = rotation +0.00015415 + other-output +0.00028865 + value/input-diagonal +0.00019861
L17H2 raw colors: A=+0.000545664, B=+0.000610698; full=+6.5034e-05 = rotation -8.5591e-05 + other-output +0.00016892 + value/input-diagonal -1.8298e-05
L17H3 raw digits: A=-0.0288521, B=-0.0293927; full=-0.00054059 = rotation -7.8209e-05 + other-output -0.00045914 + value/input-diagonal -3.2321e-06
L17H1 diag regions: A=+2952.84, B=+2964.75; full=+11.901 = rotation +1.7605 + other-output +2.7615 + value/input-diagonal +7.3785
L17H2 diag colors: A=-1065.01, B=-1053.83; full=+11.175 = rotation +1.0407 + other-output +9.1964 + value/input-diagonal +0.93808
L17H3 diag digits: A=-382.334, B=-379.876; full=+2.4579 = rotation -0.010065 + other-output +1.6729 + value/input-diagonal +0.79505

Maximum algebraic decomposition discrepancy: 1.7505996652289468e-12

=== ROTATION SIGN STABILITY UNDER REVERSING THE DECOMPOSITION ORIGIN ===
raw 48 / 48
diag 47 / 48
The unrotated remainder can also contain functional directional changes.
No causal behavioural ranking follows from this decomposition alone.
