=== VALUE-MAP READ/WRITE SUBSPACE DECOMPOSITION ===
Main analysis includes norm diagonal gains, but not hidden-state RMS denominators.
Fractions: within midpoint subspaces; outside output subspace; outside input subspace.
These are orthogonal fractions of value-map difference energy, not behavioral importance.

=== PER-LAYER ENERGY-WEIGHTED FRACTIONS ===
layer | within outside_write outside_read | aggregate_delta_norm
 0 | 0.812702 0.011483 0.175815 | 7.54983
 1 | 0.697856 0.006867 0.295277 | 90.6535
 2 | 0.879720 0.008442 0.111838 | 49.1667
 3 | 0.911264 0.012718 0.076018 | 91.5756
 4 | 0.965361 0.020012 0.014627 | 188.879
 5 | 0.779044 0.020239 0.200717 | 184.108
 6 | 0.847176 0.072726 0.080098 | 127.171
 7 | 0.805633 0.065842 0.128525 | 146.17
 8 | 0.797056 0.094973 0.107972 | 198.862
 9 | 0.780855 0.120375 0.098770 | 194.744
10 | 0.781934 0.167700 0.050365 | 459.656
11 | 0.939039 0.041313 0.019648 | 676.283
12 | 0.939029 0.053009 0.007962 | 2120.57
13 | 0.858586 0.120177 0.021237 | 1086.03
14 | 0.764667 0.199446 0.035887 | 1569.88
15 | 0.920849 0.063622 0.015529 | 2774.79
16 | 0.729805 0.252784 0.017411 | 1510.08
17 | 0.757652 0.233067 0.009281 | 988.954

Global energy-weighted fractions: [0.8702 0.1118 0.018 ]
Equal-head mean fractions: [0.8297 0.0929 0.0774]
Input/output ranks encountered: [(256, 256)]
Maximum normalized cross-inner-product: 1.0507468933963384e-15
Maximum energy closure error: 2.1094237467877974e-15
Maximum double-outside fraction: 2.034256459202832e-30

=== LARGEST OUTSIDE-INPUT FRACTIONS ===
layer head | within outside_write outside_read | relative_OV_change delta_norm
 1 3 | 0.669047 0.006322 0.324631 | 0.010402 45.1263
 1 1 | 0.677587 0.006994 0.315419 | 0.011189 45.2859
 1 2 | 0.704377 0.005258 0.290365 | 0.009673 50.8882
 1 0 | 0.751935 0.010120 0.237945 | 0.012950 39.2589
 5 0 | 0.759495 0.014246 0.226259 | 0.006763 99.2231
 0 2 | 0.769469 0.007676 0.222855 | 0.009309 4.29392
 5 3 | 0.766917 0.017747 0.215335 | 0.012132 97.3212
 5 2 | 0.788091 0.020272 0.191637 | 0.014050 92.0183
 0 0 | 0.800489 0.010484 0.189026 | 0.009090 3.69553
 0 3 | 0.810757 0.009591 0.179651 | 0.008497 3.86904
 7 1 | 0.789888 0.043237 0.166876 | 0.009481 88.8744
 8 0 | 0.799312 0.044267 0.156421 | 0.012292 140.676

=== LARGEST OUTSIDE-OUTPUT FRACTIONS ===
layer head | within outside_write outside_read | relative_OV_change delta_norm
17 1 | 0.702410 0.291779 0.005811 | 0.015686 535.714
17 3 | 0.723564 0.268307 0.008130 | 0.009954 393.374
16 1 | 0.719184 0.263177 0.017639 | 0.015624 753.964
16 3 | 0.727148 0.256698 0.016154 | 0.014510 725.911
16 0 | 0.734379 0.247324 0.018297 | 0.013532 766.217
16 2 | 0.737752 0.244813 0.017434 | 0.012551 773.196
13 2 | 0.775667 0.209741 0.014591 | 0.013600 430.244
14 2 | 0.758957 0.206636 0.034407 | 0.009846 793.92
14 0 | 0.759793 0.204696 0.035511 | 0.008382 717.892
14 1 | 0.757870 0.203922 0.038208 | 0.009365 742.592
10 2 | 0.761243 0.201608 0.037149 | 0.015041 226.06
17 2 | 0.792606 0.198168 0.009225 | 0.009836 523.678

=== LARGEST WITHIN-SUBSPACE FRACTIONS ===
layer head | within outside_write outside_read | relative_OV_change delta_norm
 4 0 | 0.967367 0.022859 0.009774 | 0.022748 85.76
 4 2 | 0.965956 0.021336 0.012708 | 0.021900 96.6511
11 2 | 0.964651 0.012766 0.022583 | 0.009668 427.04
 4 3 | 0.964564 0.015207 0.020230 | 0.015497 108.22
 4 1 | 0.963852 0.023171 0.012977 | 0.030804 85.2494
12 1 | 0.963720 0.025447 0.010832 | 0.012695 1240.98
11 3 | 0.955075 0.015922 0.029002 | 0.008268 386.675
12 2 | 0.942765 0.051226 0.006009 | 0.009621 1159.36
15 1 | 0.939187 0.038403 0.022410 | 0.016514 1636.48
15 2 | 0.927237 0.058434 0.014329 | 0.018916 1373.93
12 3 | 0.926000 0.067715 0.006285 | 0.012849 945.3
 3 1 | 0.922402 0.012235 0.065362 | 0.019785 44.2838

=== PREVIOUS CANDIDATES: GAIN-WEIGHTED VERSUS RAW GEOMETRY ===
layer head | weighted within/write/read | raw within/write/read
10 1 | 0.792406 0.167037 0.040556 | 0.450688 0.336985 0.212327
11 0 | 0.906929 0.087521 0.005549 | 0.394580 0.314751 0.290669
11 1 | 0.856291 0.140905 0.002803 | 0.480859 0.367179 0.151962
12 0 | 0.895357 0.097095 0.007548 | 0.469291 0.274586 0.256123
12 1 | 0.963720 0.025447 0.010832 | 0.456006 0.363973 0.180021
12 2 | 0.942765 0.051226 0.006009 | 0.506192 0.267921 0.225888
12 3 | 0.926000 0.067715 0.006285 | 0.458541 0.275486 0.265973
15 1 | 0.939187 0.038403 0.022410 | 0.439063 0.198227 0.362710
17 1 | 0.702410 0.291779 0.005811 | 0.442230 0.356063 0.201707

Interpretation limits:
- Midpoint subspaces are not the unavailable starting model's subspaces.
- Outside-subspace changes do not automatically represent new semantic features.
- The zero double-outside block follows algebraically from midpoint bilinearity; it is a consistency check.
- The decomposition omits attention selection and nonlinear downstream processing.
- No inputs, activations, predictions, training or checkpoint modifications were used.
