OUTPUT of run 13 of at most 60:
```
=== L17 GATE–UP–DOWN WEIGHT INTERACTION MATRICES ===
S_c = sym(G.T @ diag(D.T @ c) @ U).
c is an OUTPUT embedding contrast, not an input or hidden state.
Only parameter matrices and their products are constructed.
No S_c is evaluated on a token embedding or other proposed model input.
No GELU, gate response, hidden-state RMS, or model output is computed.
S_c describes a parameter interaction, not the full MLP function.
Relative algebraic identity discrepancy: 4.3651306363895815e-06

=== EXACT MATRIX-CHANGE DECOMPOSITION ===
geometry contrast | ||delta S|| | gate-term/total other-term/total | term cosine
raw  one_minus_nine       | 0.050158 | 0.077 0.991 | +0.074
raw  two_minus_four       | 0.042431 | 0.088 0.990 | +0.075
raw  blue_minus_red       | 0.013884 | 0.242 0.961 | +0.037
raw  white_minus_black    | 0.012201 | 0.271 0.957 | +0.021
raw  Europe_minus_Asia    | 0.012707 | 0.249 0.962 | +0.027
raw  North_minus_South    | 0.017237 | 0.215 0.969 | +0.038
diag one_minus_nine       | 2848.2 | 0.064 0.988 | +0.148
diag two_minus_four       | 2160.1 | 0.083 0.986 | +0.128
diag blue_minus_red       | 856.46 | 0.193 0.966 | +0.078
diag white_minus_black    | 683.61 | 0.261 0.954 | +0.042
diag Europe_minus_Asia    | 685.11 | 0.227 0.973 | +0.004
diag North_minus_South    | 920.89 | 0.188 0.970 | +0.063

=== VOCABULARY ASSOCIATIONS OF MATRIX EIGENDIRECTIONS ===
Eigenvalue sign belongs to B-A; each eigenvector's own sign is arbitrary.
Token labels are linear comparisons to the extracted weight directions.
raw one_minus_nine most_positive lambda=+0.012467 matrix_energy=6.18%
  +[' RUDDER':+0.290, ' HUOBI':+0.276, 'fdPar':+0.271, ' llrp':+0.270] -[' sc':-0.395, ' rec':-0.393, ' ar':-0.393, ' un':-0.392]
raw one_minus_nine most_negative lambda=-0.0066434 matrix_energy=1.75%
  +[' aumentando':+0.254, ' hemolysis':+0.249, ' escult':+0.240, ' sensores':+0.239] -[' primary':-0.296, ' meg':-0.293, ' soft':-0.291, ' network':-0.288]
raw two_minus_four most_positive lambda=+0.0098484 matrix_energy=5.39%
  +[' ret':+0.389, ' ind':+0.387, ' rec':+0.385, ' st':+0.383] -[' sparsebundle':-0.303, ' llrp':-0.290, ' Atomnoj':-0.289, ' MDET':-0.286]
raw two_minus_four most_negative lambda=-0.0076903 matrix_energy=3.28%
  +['5':+0.265, '7':+0.235, ' fin':+0.231, '4':+0.228] -[' INDI':-0.205, ' Urology':-0.204, ' joystick':-0.203, ' reeds':-0.198]
raw blue_minus_red most_positive lambda=+0.0024082 matrix_energy=3.01%
  +[' dro':+0.266, ' fin':+0.266, ' blood':+0.262, ' st':+0.261] -[' ublox':-0.230, ' Urology':-0.223, 'UO':-0.210, 'pawns':-0.207]
raw blue_minus_red most_negative lambda=-0.003107 matrix_energy=5.01%
  +[' RUDDER':+0.265, ' RxSwift':+0.258, ' HUOBI':+0.256, ' ThemeOverlay':+0.254] -[' qu':-0.359, ' al':-0.354, ' in':-0.354, ' per':-0.351]
raw white_minus_black most_positive lambda=+0.0044012 matrix_energy=13.01%
  +[' pabc':+0.286, ' permittee':+0.285, ' CodeableConcept':+0.284, ' RUDDER':+0.283] -[' rec':-0.435, ' sub':-0.422, ' st':-0.416, ' con':-0.416]
raw white_minus_black most_negative lambda=-0.0016913 matrix_energy=1.92%
  +[' ann':+0.309, ' mobile':+0.307, 'ot':+0.304, ' global':+0.302] -[' ruptura':-0.267, 'thorace':-0.253, ' DBox':-0.249, ' infrastrukt':-0.243]
raw Europe_minus_Asia most_positive lambda=+0.0017728 matrix_energy=1.95%
  +[' IGBT':+0.246, ' Fotos':+0.232, ' Epoxy':+0.225, ' Fotograf':+0.220] -[' empty':-0.316, ' common':-0.310, ' clear':-0.299, ' critical':-0.298]
raw Europe_minus_Asia most_negative lambda=-0.0044837 matrix_energy=12.45%
  +[' Vestone':+0.284, ' fxaa':+0.283, ' Appodeal':+0.283, ' CodeableConcept':+0.281] -[' sub':-0.460, ' Al':-0.451, ' ar':-0.450, ' ind':-0.444]
raw North_minus_South most_positive lambda=+0.0029384 matrix_energy=2.91%
  +[' permittee':+0.279, ' polytopes':+0.230, ' kDa':+0.229, ' lanzamiento':+0.229] -[' sub':-0.293, ' cor':-0.286, ' Sem':-0.268, ' sem':-0.261]
raw North_minus_South most_negative lambda=-0.0039401 matrix_energy=5.23%
  +[' RUDDER':+0.242, 'Casey':+0.241, ' pptd':+0.239, ' Hfn':+0.231] -[' con':-0.368, ' inter':-0.361, ' non':-0.360, ' al':-0.355]
diag one_minus_nine most_positive lambda=+1252.3 matrix_energy=19.33%
  +[' Matcha':+0.222, ' MILK':+0.220, 'BackgroundHelper':+0.219, ' Zebra':+0.212] -['4':-0.467, '7':-0.464, '8':-0.464, '6':-0.463]
diag one_minus_nine most_negative lambda=-750.54 matrix_energy=6.94%
  +[' opulent':+0.189, ' skyscrapers':+0.175, ' molecules':+0.171, ' towering':+0.167] -[' purge':-0.183, ' messa':-0.168, 'keny':-0.165, 'ovice':-0.161]
diag two_minus_four most_positive lambda=+665.88 matrix_energy=9.50%
  +[' inclusivity':+0.227, 'AnchorStyles':+0.208, 'OscInitStruct':+0.207, 'MatchType':+0.197] -['8':-0.388, '6':-0.388, '7':-0.387, '5':-0.382]
diag two_minus_four most_negative lambda=-658.32 matrix_energy=9.29%
  +[' railways':+0.196, ' canals':+0.193, ' capillaries':+0.193, ' journeys':+0.188] -['5':-0.197, '7':-0.195, '3':-0.186, '6':-0.186]
diag blue_minus_red most_positive lambda=+271.85 matrix_energy=10.07%
  +['antees':+0.171, ' Schnee':+0.167, 'Vermont':+0.165, 'stay':+0.164] -[' Playing':-0.267, 'Games':-0.222, ' Players':-0.221, ' PLAY':-0.216]
diag blue_minus_red most_negative lambda=-325.63 matrix_energy=14.46%
  +[' EnglishChoose':+0.227, 'OscInitStruct':+0.226, 'localVarPath':+0.224, 'ItemLayout':+0.220] -['8':-0.428, '6':-0.420, '7':-0.417, '4':-0.411]
diag white_minus_black most_positive lambda=+273.39 matrix_energy=15.99%
  +[' BOND':+0.207, ' Landon':+0.206, ' Acura':+0.204, ' Hoyt':+0.196] -[' the':-0.256, ' che':-0.242, ' to':-0.222, ' over':-0.221]
diag white_minus_black most_negative lambda=-154.22 matrix_energy=5.09%
  +['UK':+0.185, ' UK':+0.174, 'Maf':+0.168, ' tyre':+0.167] -[' Warcraft':-0.187, ' Whittier':-0.186, ' Wetter':-0.181, ' Peltier':-0.180]
diag Europe_minus_Asia most_positive lambda=+155.89 matrix_energy=5.18%
  +[' candidatura':+0.201, 'ensitive':+0.182, 'angor':+0.180, 'pozy':+0.178] -[' Pur':-0.221, ' Boston':-0.218, ' Minnesota':-0.218, ' Alaska':-0.216]
diag Europe_minus_Asia most_negative lambda=-297.36 matrix_energy=18.84%
  +[' the':+0.298, ' to':+0.292, ' in':+0.283, ' en':+0.278] -['localVarPath':-0.234, ' EnglishChoose':-0.220, 'OscInitStruct':-0.209, 'ClkInitStruct':-0.206]
diag North_minus_South most_positive lambda=+214.67 matrix_energy=5.43%
  +[' respiratoires':+0.167, ' decisione':+0.165, ' dnev':+0.160, 'Declar':+0.157] -[' PROM':-0.185, ' SID':-0.173, ' sociological':-0.167, ' Tob':-0.166]
diag North_minus_South most_negative lambda=-387.62 matrix_energy=17.72%
  +['7':+0.226, '6':+0.216, '8':+0.211, '3':+0.209] -[' fertiliser':-0.255, ' Watercolour':-0.248, ' privatisation':-0.245, ' modernisation':-0.238]

=== SEMANTIC ALIGNMENTS OF EXTRACTED DIRECTIONS ===
belief_minus_calculation [('diag', 'one_minus_nine', 'most_negative', -0.1027), ('raw', 'North_minus_South', 'most_positive', 0.0724), ('raw', 'North_minus_South', 'most_negative', -0.0638), ('diag', 'white_minus_black', 'most_negative', 0.0636)]
user_minus_model [('diag', 'one_minus_nine', 'most_negative', -0.0855), ('diag', 'white_minus_black', 'most_positive', -0.0703), ('diag', 'Europe_minus_Asia', 'most_positive', -0.0547), ('raw', 'two_minus_four', 'most_negative', -0.048)]
answer_minus_question [('raw', 'white_minus_black', 'most_positive', 0.0893), ('raw', 'Europe_minus_Asia', 'most_negative', 0.0837), ('diag', 'Europe_minus_Asia', 'most_negative', -0.0767), ('raw', 'North_minus_South', 'most_positive', 0.074)]
No bilinear or nonlinear response to these semantic directions is evaluated.

```