=== STORAGE TYPES ===
A: {'BF16': 235}
B: {'BF16': 235}
Skipped non-BF16 tensors: 0

=== GLOBAL ROUNDING-CELL SENSITIVITY ===
Observed difference energy: 5.857174497491531
Minimum pre-rounding difference energy allowed by independent cells: 2.754880693647009
Minimum/observed energy: 0.47034294348356015
Observed changed entries: 79105310
Entries with strictly separated rounding cells: 51516095
Separated fraction among changed entries: 0.6512343482378111

=== PER-LAYER ROUNDING-CELL SENSITIVITY ===
layer | minimum/observed energy | separated fraction among changed entries
-1 unchanged stored values
 0 | 0.4227186 | 0.6101061
 1 | 0.4591072 | 0.6453167
 2 | 0.4341586 | 0.6232620
 3 | 0.4775525 | 0.6628341
 4 | 0.4945406 | 0.6774883
 5 | 0.4708230 | 0.6480958
 6 | 0.4732807 | 0.6560157
 7 | 0.4602388 | 0.6421157
 8 | 0.4737407 | 0.6603007
 9 | 0.4628094 | 0.6412732
10 | 0.4831312 | 0.6621477
11 | 0.4674089 | 0.6506781
12 | 0.4774928 | 0.6533619
13 | 0.4869913 | 0.6627688
14 | 0.4877733 | 0.6634494
15 | 0.4726797 | 0.6494665
16 | 0.4739269 | 0.6512888
17 | 0.4788637 | 0.6591909

=== CANDIDATE SUBSPACE ROBUSTNESS ===
The minimum-separation array is a diagnostic, not an estimate of the actual unrounded update.
layer tensor | retained_energy | effective_rank_original minimum | top16_subspace_overlap | top1_energy_original minimum
10 mlp.down_proj           | 0.684757 |    35.667    41.010 | 0.993131 | 0.116543 0.106261
10 self_attn.q_proj        | 0.510843 |    14.150    15.022 | 0.913509 | 0.211505 0.211729
11 self_attn.k_proj        | 0.526683 |    15.613    19.557 | 0.903000 | 0.155254 0.146728
12 mlp.down_proj           | 0.588788 |    58.674    72.422 | 0.977506 | 0.073567 0.062638
12 self_attn.q_proj        | 0.552030 |    12.156    14.357 | 0.903933 | 0.243115 0.218660
14 mlp.down_proj           | 0.694498 |    74.464    81.190 | 0.996037 | 0.048405 0.046385
15 self_attn.o_proj        | 0.449769 |    55.999    75.053 | 0.964138 | 0.060619 0.050598
15 self_attn.v_proj        | 0.397003 |    34.771    47.778 | 0.894647 | 0.109648 0.089329
16 mlp.down_proj           | 0.627314 |    40.414    46.859 | 0.996517 | 0.088813 0.081550
 2 mlp.down_proj           | 0.630963 |    69.509    79.657 | 0.989344 | 0.050013 0.045935
 3 mlp.gate_proj           | 0.404189 |    58.594    83.218 | 0.906130 | 0.073971 0.060251

=== MATRIX TENSORS MOST SENSITIVE TO ROUNDING-CELL SHRINKAGE ===
model.layers.0.self_attn.v_proj.weight retained_energy= 0.3383341908682808 separated_fraction= 0.5381885071765377
model.layers.3.self_attn.v_proj.weight retained_energy= 0.3480086303182185 separated_fraction= 0.5459018065020478
model.layers.7.self_attn.v_proj.weight retained_energy= 0.34848639741183934 separated_fraction= 0.5445322273825641
model.layers.2.self_attn.v_proj.weight retained_energy= 0.3534171878839408 separated_fraction= 0.5520382965453886
model.layers.1.self_attn.v_proj.weight retained_energy= 0.3582974930275512 separated_fraction= 0.5562901667576763
model.layers.2.mlp.up_proj.weight retained_energy= 0.36016049952379725 separated_fraction= 0.5531271907387408
model.layers.8.self_attn.v_proj.weight retained_energy= 0.3607938724553992 separated_fraction= 0.5539574417799836
model.layers.1.mlp.up_proj.weight retained_energy= 0.361910811971699 separated_fraction= 0.5570757987386078
model.layers.4.self_attn.v_proj.weight retained_energy= 0.36307502039211353 separated_fraction= 0.559539213873998
model.layers.0.mlp.up_proj.weight retained_energy= 0.3636578488424407 separated_fraction= 0.5594795110163946
model.layers.2.mlp.gate_proj.weight retained_energy= 0.36482396184246735 separated_fraction= 0.557731139674594
model.layers.9.self_attn.v_proj.weight retained_energy= 0.364913766782749 separated_fraction= 0.5559321460870741
model.layers.1.mlp.gate_proj.weight retained_energy= 0.3655898087543802 separated_fraction= 0.5586303552121047
model.layers.6.self_attn.v_proj.weight retained_energy= 0.3676708028919256 separated_fraction= 0.557844106655047
model.layers.0.mlp.gate_proj.weight retained_energy= 0.36863993787939037 separated_fraction= 0.561283751707061

Interpretation limits:
- Rounding cells assume round-to-nearest BF16; actual training/storage history is unknown.
- Touching cell boundaries give zero infimum separation; tie-breaking does not affect that bound.
- The energy bound concerns weights, not attention maps, activations, logits or behavioral effects.
- Eigenvectors of the minimum-separation array are not bounds on unknown true-update eigenvectors.
- No model inputs, nonlinearities, training, or checkpoint modifications were used.
