=== ROTARY GAIN/PHASE EXPLANATION TEST ===
Independent amplitude and phase projections are orthogonal in coefficient-pair space.
Their residual is change not explained by those two directions.
The coherent-shift projection is a restricted subspace of the independent phase directions.
All operations concern coefficient matrices, not scores at positions or inputs.

=== PER-LAYER ENERGY-WEIGHTED FRACTIONS ===
layer | independent_gain independent_phase residual | coherent_shift uniform_gain
 0 | 0.00295056 0.00106919 0.99598026 | 0.00000745 0.00002759
 1 | 0.00267626 0.00076034 0.99656340 | 0.00001253 0.00001347
 2 | 0.00188707 0.00097721 0.99713572 | 0.00002486 0.00000218
 3 | 0.00203888 0.00159388 0.99636725 | 0.00000537 0.00001543
 4 | 0.00779507 0.00065253 0.99155240 | 0.00000791 0.00008237
 5 | 0.00421084 0.00212030 0.99366886 | 0.00000015 0.00017302
 6 | 0.00432001 0.00183444 0.99384555 | 0.00001160 0.00003743
 7 | 0.00416153 0.00077246 0.99506601 | 0.00000287 0.00005034
 8 | 0.00592516 0.00083104 0.99324380 | 0.00000396 0.00000442
 9 | 0.00679933 0.00133198 0.99186868 | 0.00000094 0.00019580
10 | 0.00868315 0.00162332 0.98969353 | 0.00000317 0.00014988
11 | 0.01620442 0.00661107 0.97718451 | 0.00006247 0.00032333
12 | 0.01239058 0.00592966 0.98167976 | 0.00000753 0.00035477
13 | 0.01284777 0.00464018 0.98251205 | 0.00004624 0.00014136
14 | 0.01797935 0.00372726 0.97829339 | 0.00001602 0.00002983
15 | 0.01564669 0.00368975 0.98066357 | 0.00004684 0.00018623
16 | 0.01564933 0.00458150 0.97976916 | 0.00003662 0.00015061
17 | 0.01478217 0.00588918 0.97932865 | 0.00000266 0.00048515

=== HEADS MOST EXPLAINED BY INDEPENDENT PHASE CHANGES ===
layer head | phase gain residual | coherent_shift_fraction shift_projection_coefficient
11 2 | 0.00916832 0.01544857 0.97538311 | 0.00001006 +0.004617584
17 3 | 0.00737786 0.01143408 0.98118806 | 0.00000399 +0.002276447
11 3 | 0.00654492 0.01240128 0.98105380 | 0.00002114 +0.0024542343
12 3 | 0.00632728 0.01138524 0.98228748 | 0.00000020 +0.00036869246
17 1 | 0.00628262 0.01527447 0.97844291 | 0.00000660 -0.00058797787
16 3 | 0.00611737 0.01670351 0.97717913 | 0.00000155 -0.00017341784
12 1 | 0.00588232 0.01104655 0.98307113 | 0.00001119 +0.0026945584
11 0 | 0.00579371 0.01398296 0.98022333 | 0.00004187 +0.0020325995
12 2 | 0.00577850 0.01118675 0.98303475 | 0.00000095 +0.00066171632
12 0 | 0.00575637 0.01542043 0.97882320 | 0.00001616 +0.0028580215
11 1 | 0.00572831 0.02233077 0.97194092 | 0.00015617 +0.0018723275
17 2 | 0.00564287 0.02308523 0.97127190 | 0.00000030 +0.00082825286
13 0 | 0.00535986 0.01522899 0.97941115 | 0.00004032 +0.00079618851
16 0 | 0.00533907 0.01435361 0.98030732 | 0.00001687 -0.00032817731
13 3 | 0.00481801 0.01074546 0.98443653 | 0.00000628 +0.00085025615
17 0 | 0.00470371 0.00678740 0.98850889 | 0.00000000 -2.0623593e-05

=== HEADS MOST EXPLAINED BY A COHERENT POSITION-SHIFT DIRECTION ===
layer=11 head=1 shift_fraction=0.000156167 shift_coefficient=+0.0018723275
layer=15 head=1 shift_fraction=0.000136158 shift_coefficient=-0.0016438091
layer=16 head=1 shift_fraction=0.000083509 shift_coefficient=-0.00051071932
layer=13 head=2 shift_fraction=0.000075552 shift_coefficient=+0.00076280055
layer=13 head=1 shift_fraction=0.000072753 shift_coefficient=+0.00071463917
layer= 2 head=1 shift_fraction=0.000054776 shift_coefficient=-0.00070234067
layer=15 head=2 shift_fraction=0.000045542 shift_coefficient=-0.00083186752
layer=11 head=0 shift_fraction=0.000041868 shift_coefficient=+0.0020325995
layer=13 head=0 shift_fraction=0.000040325 shift_coefficient=+0.00079618851
layer=16 head=2 shift_fraction=0.000039496 shift_coefficient=-0.00050026781
A shift coefficient with negligible explained energy is not evidence of an actual attention-distance shift.

=== PREVIOUS ROTARY CANDIDATES: INDIVIDUAL FREQUENCIES ===
layer=11 head=0 pair= 88 head_change_energy_share=0.256469 gain_explained=0.02637531 phase_explained=0.00283350 phase_projection=+0.0021940328
layer=11 head=1 pair= 88 head_change_energy_share=0.175016 gain_explained=0.06699611 phase_explained=0.00506967 phase_projection=+0.0030602438
layer=12 head=0 pair=111 head_change_energy_share=0.073314 gain_explained=0.01249802 phase_explained=0.00267336 phase_projection=+0.0019022737
layer=12 head=2 pair=111 head_change_energy_share=0.057010 gain_explained=0.01896315 phase_explained=0.00560256 phase_projection=-0.0014933679
layer=17 head=1 pair= 87 head_change_energy_share=0.179282 gain_explained=0.00051377 phase_explained=0.00068500 phase_projection=+0.00072055044
layer=10 head=1 pair= 75 head_change_energy_share=0.091047 gain_explained=0.02068414 phase_explained=0.00075954 phase_projection=-0.00073749861

=== CONSISTENCY CHECKS ===
Minimum residual fraction: 0.9641598115549526
Maximum coherent-shift minus independent-phase fraction: -0.0005759230668247598

Interpretation limits:
- The projections describe midpoint coefficient geometry, not evaluated attention behavior.
- They do not include query/key hidden-state RMS denominators or softmax competition.
- Residual change need not represent a new semantic feature; it only excludes these simple explanations.
- A positional projection cannot identify where the user's guess occurs.
- No inputs, positions, activations, model execution, training or checkpoint modifications were used.
