=== GLOBAL NONLINEAR NUMERATOR DIFFERENCE BOUNDS ===
For every vector x, the unit numerator difference is bounded by b_i*||x||^2.
No x is constructed or evaluated.
Bounds include stored diagonal gains but exclude RMS denominators.
The sum over units is a valid, potentially loose, whole-numerator bound.
A larger bound does not establish a larger actual effect.

=== LAYER BOUND COEFFICIENTS ===
layer | total_bound coefficient / baseline_upper_bound | down/gate/up/interaction shares | top10 bound share
 0 |      4860.34 0.0354667 | 0.540194 0.296659 0.163138 0.000009 | 0.023826
 1 |       178158 0.0423551 | 0.604174 0.255772 0.140044 0.000010 | 0.013592
 2 |       221259 0.0337899 | 0.508320 0.319244 0.172427 0.000008 | 0.015151
 3 |       573985 0.0426392 | 0.528173 0.324640 0.147175 0.000012 | 0.016903
 4 |       128405 0.0432506 | 0.604504 0.259755 0.135730 0.000011 | 0.024292
 5 |       167611 0.0300253 | 0.403622 0.395848 0.200523 0.000008 | 0.019295
 6 |      71056.7 0.0312579 | 0.436697 0.376156 0.187140 0.000008 | 0.021151
 7 |      62996.7 0.0291416 | 0.385494 0.412588 0.201911 0.000007 | 0.016523
 8 |      48267.7 0.0358936 | 0.492768 0.341284 0.165939 0.000009 | 0.019125
 9 |      32099.5 0.0305602 | 0.387893 0.409177 0.202923 0.000007 | 0.012891
10 |      82138.8 0.0353077 | 0.487752 0.343658 0.168581 0.000009 | 0.021147
11 |       332014 0.0285573 | 0.386738 0.407240 0.206015 0.000007 | 0.013939
12 |       211182 0.0295851 | 0.368594 0.415101 0.216297 0.000007 | 0.011829
13 |       170228 0.0339103 | 0.453476 0.356862 0.189653 0.000009 | 0.012832
14 |       163595 0.0366109 | 0.478128 0.343093 0.178770 0.000010 | 0.011394
15 |       116986 0.0348179 | 0.444179 0.366137 0.189675 0.000009 | 0.010776
16 |       130856 0.0334278 | 0.422536 0.380655 0.196800 0.000009 | 0.011891
17 |       139967 0.0356324 | 0.414787 0.393231 0.191972 0.000010 | 0.012164
The baseline ratio compares two bounds, not actual output norms.

=== RANKING AGREEMENT WITH PER-UNIT COEFFICIENT CHANGES ===
layer | top10 overlap with degrees 2/3/5 | rank correlations with degrees 2/3/5 | top5 bound units
 0 |  8  8  7 | 0.95472 0.93286 0.79967 | [1405, 1130, 878, 1856, 1352]
 1 |  3  6  6 | 0.95399 0.94157 0.84301 | [239, 990, 702, 835, 1195]
 2 |  7  5  3 | 0.94220 0.92363 0.79845 | [1831, 700, 1710, 925, 918]
 3 |  5  4  2 | 0.95166 0.84337 0.70543 | [1414, 1635, 226, 95, 2019]
 4 |  9  8  4 | 0.95240 0.90847 0.79109 | [84, 13, 1044, 1830, 1400]
 5 |  5  2  1 | 0.95430 0.86304 0.70473 | [584, 1759, 725, 501, 1597]
 6 |  7  5  4 | 0.94406 0.85376 0.68165 | [1824, 1122, 314, 492, 43]
 7 |  3  2  1 | 0.93376 0.75920 0.54091 | [1455, 1057, 348, 70, 664]
 8 |  7  5  4 | 0.93635 0.82878 0.70185 | [188, 1394, 1558, 487, 522]
 9 |  6  3  3 | 0.93743 0.76160 0.61031 | [385, 437, 1579, 448, 1782]
10 |  7  6  5 | 0.96051 0.86036 0.75867 | [1363, 1564, 1529, 1016, 1106]
11 |  5  4  3 | 0.97615 0.89261 0.79048 | [1892, 387, 896, 662, 611]
12 |  5  3  2 | 0.96501 0.83052 0.68944 | [1528, 1520, 244, 22, 259]
13 |  6  6  5 | 0.93387 0.78697 0.65289 | [16, 1575, 1517, 1059, 859]
14 |  8  6  6 | 0.93024 0.76310 0.61117 | [641, 1260, 663, 392, 1666]
15 |  5  3  2 | 0.92195 0.72322 0.54550 | [1226, 1369, 651, 2037, 1966]
16 |  8  8  5 | 0.92391 0.68595 0.47650 | [1591, 893, 730, 287, 324]
17 |  5  5  4 | 0.89167 0.59107 0.36198 | [1650, 1026, 77, 1916, 620]

=== PREVIOUS CANDIDATES UNDER THE NONLOCAL BOUND ===
layer unit | bound_rank coefficient_ranks_2_3_5 | share_of_layer_bound | down/gate/up/interaction bound shares
 2 1831 |    1 [1, 1, 1] | 0.0024144 | 0.873571 0.055349 0.071074 0.000005
 3   82 |   14 [4, 1, 1] | 0.0012402 | 0.724786 0.073167 0.202041 0.000007
 3 1414 |    1 [1, 20, 323] | 0.0032971 | 0.068862 0.821092 0.110045 0.000001
 3 1671 |   30 [5, 2, 2] | 0.0011134 | 0.697639 0.119951 0.182404 0.000006
10 1363 |    1 [1, 1, 1] | 0.0041700 | 0.847622 0.059991 0.092385 0.000001
10 1529 |    3 [3, 3, 2] | 0.0023179 | 0.873992 0.052414 0.073593 0.000001
10 1564 |    2 [2, 2, 3] | 0.0035392 | 0.716571 0.116631 0.166797 0.000001
12  259 |    5 [3, 9, 19] | 0.0011496 | 0.515840 0.234537 0.249618 0.000005
12 1520 |    2 [2, 2, 3] | 0.0012743 | 0.505794 0.120064 0.374138 0.000004
12 1528 |    1 [1, 1, 1] | 0.0014315 | 0.558791 0.082394 0.358813 0.000002
12 1584 |   34 [9, 3, 2] | 0.0009514 | 0.506231 0.152490 0.341277 0.000002
16  893 |    2 [1, 1, 1] | 0.0018570 | 0.644976 0.132239 0.222783 0.000002

=== MOST CONCENTRATED UNIT BOUNDS RELATIVE TO THEIR OWN LAYERS ===
layer= 5 unit= 584 bound_share=0.0059145 coefficient_ranks=[1, 1, 3]
layer= 0 unit=1405 bound_share=0.0050887 coefficient_ranks=[2, 3, 4]
layer= 8 unit= 188 bound_share=0.0042918 coefficient_ranks=[1, 13, 244]
layer=10 unit=1363 bound_share=0.0041700 coefficient_ranks=[1, 1, 1]
layer= 6 unit=1824 bound_share=0.0040963 coefficient_ranks=[2, 2, 1]
layer= 4 unit=  84 bound_share=0.0038360 coefficient_ranks=[5, 56, 384]
layer= 0 unit=1130 bound_share=0.0038157 coefficient_ranks=[1, 1, 1]
layer= 6 unit=1122 bound_share=0.0036754 coefficient_ranks=[1, 1, 2]
layer=10 unit=1564 bound_share=0.0035392 coefficient_ranks=[2, 2, 3]
layer= 3 unit=1414 bound_share=0.0032971 coefficient_ranks=[1, 20, 323]
layer= 4 unit=  13 bound_share=0.0031049 coefficient_ranks=[12, 4, 5]
layer= 4 unit=1044 bound_share=0.0029716 coefficient_ranks=[1, 1, 3]
layer= 7 unit=1455 bound_share=0.0029498 coefficient_ranks=[1, 1, 2]
layer= 0 unit= 878 bound_share=0.0028000 coefficient_ranks=[4, 4, 3]
layer= 4 unit=1830 bound_share=0.0024373 coefficient_ranks=[6, 8, 19]
layer= 2 unit=1831 bound_share=0.0024144 coefficient_ranks=[1, 1, 1]
layer=10 unit=1529 bound_share=0.0023179 coefficient_ranks=[3, 3, 2]
layer= 7 unit=1057 bound_share=0.0023174 coefficient_ranks=[2, 6, 13]
layer= 0 unit=1856 bound_share=0.0023028 coefficient_ranks=[3, 2, 2]
layer= 4 unit=1400 bound_share=0.0021600 coefficient_ranks=[7, 6, 13]

Interpretation limits:
- These are upper bounds, not estimates, lower bounds, activation measurements or causal effects.
- Summing unit bounds discards cancellations and need not be tight.
- The actual normalized MLP output is not bounded here by the same coefficient without additional analysis.
- Agreement between bound and coefficient rankings does not identify semantic functions.
- Only weight norms, inner products and symbolic inequalities were used.
