=== SCALE-CANONICAL ATTENTION SCORING FORMS ===
M = Q^T diag(q_gain*k_gain) K; P = Q^T Q; R = K^T K.
Input norm diagonal gains are folded into Q and K.
Canonical forms: M/sqrt(tr(P)tr(R)), P/tr(P), R/tr(R).
These retain zero-offset normalized-score geometry in the zero-epsilon limit.
They are not attention scores evaluated on any inputs.

Largest equal-weight RMS relative changes of the three forms:
layer head | joint numerator query_metric key_metric | uncanonicalized_numerator
11  0 | 0.0267984 0.0455889 0.0038082 0.0078500 | 0.0455931
11  1 | 0.0247122 0.0417940 0.0048694 0.0078500 | 0.0417968
10  1 | 0.0190206 0.0325586 0.0026235 0.0042897 | 0.0325590
12  2 | 0.0168346 0.0283502 0.0046054 0.0050265 | 0.0283502
11  3 | 0.0162431 0.0263886 0.0057909 0.0078500 | 0.0263827
12  0 | 0.0161861 0.0256629 0.0101054 0.0050265 | 0.0256404
17  1 | 0.0160195 0.0273648 0.0037017 0.0027096 | 0.0273700
14  1 | 0.0153367 0.0261548 0.0031725 0.0033910 | 0.0261560
12  3 | 0.0146191 0.0244390 0.0043150 0.0050265 | 0.0244463
14  3 | 0.0139734 0.0237314 0.0033309 0.0033910 | 0.0237312
 5  3 | 0.0138883 0.0233304 0.0052688 0.0025663 | 0.0233333
14  0 | 0.0136545 0.0231949 0.0031360 0.0033910 | 0.0231924
 5  0 | 0.0136384 0.0231375 0.0040109 0.0025663 | 0.0231375
10  0 | 0.0131045 0.0218250 0.0045219 0.0042897 | 0.0218250
13  1 | 0.0130327 0.0221136 0.0035047 0.0028735 | 0.0221136
 6  2 | 0.0129365 0.0218390 0.0033029 0.0037690 | 0.0218390
12  1 | 0.0128534 0.0206475 0.0066367 0.0050265 | 0.0206510
13  2 | 0.0127158 0.0216665 0.0027161 0.0028735 | 0.0216672
11  2 | 0.0121554 0.0179615 0.0076824 0.0078500 | 0.0179640
15  0 | 0.0121515 0.0202571 0.0040623 0.0040156 | 0.0202584
14  2 | 0.0117580 0.0198612 0.0029644 0.0033910 | 0.0198639
 7  3 | 0.0116196 0.0193256 0.0030230 0.0047361 | 0.0193256
17  0 | 0.0115425 0.0193419 0.0042709 0.0027096 | 0.0193397
 9  2 | 0.0110962 0.0183167 0.0036211 0.0045564 | 0.0183173

=== LAYER SUMMARY: MEAN RELATIVE FORM CHANGES OVER HEADS ===
layer | numerator query_metric key_metric
 0 | 0.0097589 0.0032496 0.0034648
 1 | 0.0113076 0.0035836 0.0053121
 2 | 0.0108783 0.0040304 0.0053785
 3 | 0.0112415 0.0045682 0.0042777
 4 | 0.0145043 0.0026233 0.0033968
 5 | 0.0196076 0.0047672 0.0025663
 6 | 0.0169255 0.0044181 0.0037690
 7 | 0.0157268 0.0036645 0.0047361
 8 | 0.0138075 0.0039574 0.0039271
 9 | 0.0155608 0.0037114 0.0045564
10 | 0.0203682 0.0041223 0.0042897
11 | 0.0329332 0.0055377 0.0078500
12 | 0.0247749 0.0064156 0.0050265
13 | 0.0182225 0.0038541 0.0028735
14 | 0.0232356 0.0031509 0.0033910
15 | 0.0163713 0.0043350 0.0040156
16 | 0.0156211 0.0025078 0.0031142
17 | 0.0175291 0.0043018 0.0027096

=== EXACT NUMERATOR FACTOR ATTRIBUTIONS FOR TOP ROUTING CANDIDATES ===
Signed shares: Q/input, K/input, q_norm gain, k_norm gain, third-order interaction.
11  0 | +0.2766033 +0.7233136 +0.0000556 +0.0000275 +0.0000000
11  1 | +0.2325248 +0.7674674 +0.0000119 -0.0000041 -0.0000000
10  1 | +0.5596690 +0.4401785 +0.0000470 +0.0001055 +0.0000000
12  2 | +0.7763304 +0.2236818 +0.0000143 -0.0000265 +0.0000000
11  3 | +0.3121847 +0.6876951 +0.0001162 +0.0000040 +0.0000000
12  0 | +0.7515660 +0.2483880 +0.0000672 -0.0000212 +0.0000000
17  1 | +0.6475747 +0.3524172 +0.0000264 -0.0000184 +0.0000000
14  1 | +0.7708759 +0.2293028 -0.0001858 +0.0000070 +0.0000000
12  3 | +0.7622122 +0.2377138 +0.0001049 -0.0000310 -0.0000000
14  3 | +0.7446326 +0.2553163 -0.0000690 +0.0001200 +0.0000000
 5  3 | +0.8363814 +0.1635874 +0.0000312 +0.0000000 +0.0000000
14  0 | +0.7843566 +0.2152780 +0.0001901 +0.0001752 +0.0000000
 5  0 | +0.8171519 +0.1828069 +0.0000412 +0.0000000 -0.0000000
10  0 | +0.5795877 +0.4202756 +0.0001589 -0.0000221 +0.0000000
13  1 | +0.4612128 +0.5386058 +0.0001644 +0.0000170 +0.0000000
 6  2 | +0.4329822 +0.5667867 +0.0001299 +0.0001012 +0.0000000
12  1 | +0.6875932 +0.3123215 +0.0001402 -0.0000550 +0.0000000
13  2 | +0.4445015 +0.5554210 +0.0000302 +0.0000474 +0.0000000
11  2 | +0.4446416 +0.5553455 +0.0000075 +0.0000054 -0.0000000
15  0 | +0.4938909 +0.5058378 +0.0002138 +0.0000574 +0.0000000

Largest reconstruction error: 3.3832172479216686e-14
Maximum Q radial fraction: 0.0024304230713184404
Maximum K radial fraction: 0.0002565888064727726

Cautions:
- Equal-weight joint ranking is a descriptive convention, not an importance measure.
- Key geometry is shared across all four heads in a layer.
- Epsilon terms, nonzero rotary offsets, softmax competition, and actual positions are not evaluated.
- No construction here identifies question, guess, answer, or correctness features.
