GRAMMATICAL/SEMANTIC CONTROL GROUPS
original_belief ['think', 'believe', 'guess', 'suppose', 'suspect', 'reckon', 'opinion', 'assume']
new_belief_verbs ['presume', 'imagine', 'expect', 'infer', 'estimate', 'doubt', 'feel', 'conjecture']
ordinary_verbs ['walk', 'read', 'write', 'open', 'close', 'make', 'build', 'carry']
knowledge_verbs ['know', 'understand', 'prove', 'verify', 'check', 'confirm', 'recognize', 'remember']
belief_nouns ['belief', 'opinion', 'assumption', 'estimate', 'hunch', 'intuition', 'impression', 'feeling']
fact_nouns ['fact', 'evidence', 'proof', 'reason', 'logic', 'knowledge', 'information', 'truth']
instruction_verbs ['calculate', 'determine', 'solve', 'identify', 'find', 'choose', 'select', 'explain']
question_words ['which', 'what', 'where', 'when', 'who', 'how', 'why']

DIRECTIONAL LEXICAL CONTROLS
B-A key coupling for the answer-query template, standardized by
its variation across vocabulary-weight rows. Not attention probabilities.
Columns: ['original_belief', 'new_belief_verbs', 'ordinary_verbs', 'knowledge_verbs', 'belief_nouns', 'fact_nouns', 'instruction_verbs', 'question_words']
L00 H3:  +1.544  +1.157  -0.536  +0.970  +0.790  +0.900  +0.498  -0.160
  belief verbs minus ordinary verbs: 1.693 ; belief nouns minus fact nouns: -0.11
L01 H1:  -0.330  -0.007  -0.004  -0.628  -1.070  -0.275  -0.278  +1.622
  belief verbs minus ordinary verbs: -0.003 ; belief nouns minus fact nouns: -0.795
L05 H0:  +1.159  +0.878  -0.013  -0.114  +1.054  +0.241  -0.104  -0.280
  belief verbs minus ordinary verbs: 0.89 ; belief nouns minus fact nouns: 0.813
L16 H3:  +0.807  +0.519  +0.346  +0.738  +0.432  +0.355  +0.482  -0.661
  belief verbs minus ordinary verbs: 0.173 ; belief nouns minus fact nouns: 0.077
L17 H2:  +0.613  +0.372  +0.392  -0.376  +0.308  +0.085  +0.651  +1.287
  belief verbs minus ordinary verbs: -0.02 ; belief nouns minus fact nouns: 0.222

UNSUPERVISED FACTORS OF THE VOCABULARY-VISIBLE QK DIFFERENCE
Each positive singular term adds B coupling for query+/key+ and query-/key-.
It subtracts B coupling for opposite signs. This is a matrix identity,
not a claim that the model attends to these tokens in context.

L00 H3: QK energy fractions=[0.3992 0.2116 0.1793]; raw query-delta first energy=0.2081; raw leading-singular-value/sign-control=4.173
 factor 1
  query +: [("' Tanzania'", 3.7), ("' Bolivia'", 3.67), ("' Bulgaria'", 3.66), ("' Argentina'", 3.55), ("' Kenya'", 3.53), ("' Shanghai'", 3.49)]
  query -: [("' is'", -4.89), ("' are'", -4.52), ("' cortos'", -3.84), ("' farlo'", -3.74), ("' prvo'", -3.72), ("'etary'", -3.69)]
  key +: [("'conder'", 3.93), ("' lentamente'", 3.84), ("' Yemeni'", 3.79), ("' especificar'", 3.62), ("'adka'", 3.53), ("' graduellement'", 3.51)]
  key -: [("' New'", -4.81), ("' what'", -4.62), ("' What'", -4.29), ("' Red'", -4.05), ("' St'", -4.04), ("' Blue'", -4.03)]
 complete delta, answer-query -> keys +: [("'The'", 4.79), ("' mortars'", 4.34), ("'hesia'", 4.33), ("'adka'", 4.3), ("' dihedral'", 4.11), ("'effici'", 3.97), ("' radiographs'", 3.97)]
 complete delta, answer-query -> keys -: [("' is'", -4.91), ("' Island'", -4.34), ("' island'", -4.06), ("'van'", -4.06), ("' New'", -4.04), ("' ark'", -3.86), ("' Is'", -3.86)]
 factor 2
  query +: [("'constraintStart'", 4.12), ("'MiddleCenter'", 3.68), ("' Bong'", 3.64), ("' Newtown'", 3.63), ("' INTEGER'", 3.62), ("'ToRemove'", 3.6)]
  query -: [("' is'", -5.54), ("' since'", -4.6), ("'hrer'", -4.58), ("'ly'", -4.49), ("'ed'", -4.46), ("' identity'", -4.42)]
  key +: [("' German'", 4.49), ("' Somali'", 4.25), ("' French'", 4.17), ("' Saudi'", 4.14), ("' Turkish'", 4.12), ("' Senegal'", 4.03)]
  key -: [("'nPortIndex'", -4.02), ("'HasStarred'", -4.02), ("'WithFieldContext'", -4.0), ("' sAlarm'", -3.93), ("' addCriterion'", -3.91), ("' tagReport'", -3.9)]

L01 H1: QK energy fractions=[0.2116 0.1013 0.0721]; raw query-delta first energy=0.1296; raw leading-singular-value/sign-control=3.096
 factor 1
  query +: [("' banana'", 7.2), ("' bananas'", 5.23), ("'banana'", 5.07), ("' Banana'", 4.52), ("'Banana'", 4.42), ("'chin'", 4.31)]
  query -: [("' tampoco'", -4.61), ("' perjud'", -4.5), ("' erau'", -4.39), ("'iaio'", -4.17), ("' foarte'", -4.09), ("' voj'", -3.89)]
  key +: [("' enfri'", 3.82), ("' emitida'", 3.74), ("' banderas'", 3.45), ("' attraverso'", 3.41), ("' oficiales'", 3.37), ("' opnieuw'", 3.32)]
  key -: [("' banana'", -7.57), ("' Banana'", -5.75), ("' bananas'", -5.65), ("' fruit'", -5.06), ("' sugar'", -4.96), ("'banana'", -4.87)]
 complete delta, answer-query -> keys +: [("'eraient'", 4.95), ("' those'", 4.67), ("' than'", 4.5), ("' that'", 4.2), ("' my'", 4.16), ("' couldn'", 4.14), ("' putea'", 4.09)]
 complete delta, answer-query -> keys -: [("' Belarus'", -4.89), ("' Palau'", -4.74), ("' banana'", -4.15), ("' Banana'", -4.12), ("'Europe'", -4.1), ("' Nepal'", -4.1), ("' Dirac'", -4.06)]

L05 H0: QK energy fractions=[0.3276 0.1062 0.08  ]; raw query-delta first energy=0.3163; raw leading-singular-value/sign-control=4.576
 factor 1
  query +: [("'Alexander'", 4.71), ("' Rach'", 4.59), ("' COLUMN'", 4.48), ("'Opinion'", 4.38), ("'Pda'", 4.37), ("' protons'", 4.37)]
  query -: [("' turmeric'", -4.33), ("'inim'", -4.32), ("' Demir'", -4.21), ("' glider'", -4.2), ("' Wiggins'", -4.18), ("' denominador'", -4.14)]
  key +: [("' MRD'", 5.41), ("' Waugh'", 4.91), ("' Andover'", 4.7), ("' MND'", 4.62), ("'odt'", 4.59), ("' mydict'", 4.58)]
  key -: [("' Lay'", -5.4), ("' Leno'", -5.24), ("' Simons'", -5.04), ("' Lap'", -5.01), ("' Summers'", -4.98), ("' Hamlin'", -4.88)]
 complete delta, answer-query -> keys +: [("'Supply'", 4.83), ("'ibut'", 4.57), ("' Minerva'", 4.51), ("' Supply'", 4.5), ("'PHIL'", 4.41), ("' Rapt'", 4.32), ("' SUPPLY'", 4.28)]
 complete delta, answer-query -> keys -: [("' Kah'", -5.09), ("' Campbell'", -4.97), ("'dek'", -4.95), ("' Carroll'", -4.68), ("' Hui'", -4.64), ("' Osc'", -4.6), ("' Kearns'", -4.59)]

L16 H3: QK energy fractions=[0.3656 0.1316 0.0844]; raw query-delta first energy=0.1740; raw leading-singular-value/sign-control=3.799
 factor 1
  query +: [("'segaretro'", 4.74), ("' rebounded'", 4.72), ("' misplaced'", 4.7), ("'false'", 4.57), ("'Modular'", 4.21), ("'Tracks'", 4.16)]
  query -: [("'ting'", -4.99), ("'autre'", -4.93), ("'tai'", -4.55), ("'gado'", -4.48), ("' marg'", -4.44), ("'atet'", -4.43)]
  key +: [("'YK'", 4.31), ("'abc'", 4.29), ("' pozosta'", 4.05), ("'ajaran'", 4.03), ("'eight'", 3.94), ("' mengapa'", 3.87)]
  key -: [("' Railway'", -4.29), ("' Indicator'", -4.23), ("' mascara'", -4.21), ("' fishermen'", -4.14), ("' wafer'", -4.13), ("' Ness'", -4.12)]
 complete delta, answer-query -> keys +: [("' Natl'", 4.83), ("' Gazette'", 4.7), ("' nervoso'", 4.67), ("'cine'", 4.6), ("' theatres'", 4.27), ("'antry'", 4.26), ("'crets'", 4.24)]
 complete delta, answer-query -> keys -: [("'Charged'", -4.31), ("' Erickson'", -4.27), ("'waarden'", -4.2), ("'utherford'", -4.1), ("'Diamonds'", -3.93), ("' rebound'", -3.91), ("'rau'", -3.89)]

L17 H2: QK energy fractions=[0.3936 0.1472 0.0991]; raw query-delta first energy=0.2184; raw leading-singular-value/sign-control=3.792
 factor 1
  query +: [("'Pep'", 4.64), ("' stroll'", 4.6), ("'Constit'", 4.47), ("'PEP'", 4.39), ("' sno'", 4.36), ("' Bernad'", 4.32)]
  query -: [("' voegen'", -4.59), ("' imageName'", -4.49), ("' otp'", -4.43), ("' Crowe'", -4.1), ("'unehmen'", -4.01), ("' Naik'", -3.98)]
  key +: [("'ly'", 4.95), ("'ia'", 4.56), ("'he'", 4.48), ("' in'", 4.3), ("'ian'", 4.28), ("' and'", 4.28)]
  key -: [("'Ampl'", -3.88), ("'TabPage'", -3.63), ("' EnglishChoose'", -3.56), ("' Rwand'", -3.47), ("'ItemLayout'", -3.43), ("' Igu'", -3.4)]
 complete delta, answer-query -> keys +: [("'th'", 5.21), ("'to'", 4.49), ("'ly'", 4.1), ("'ast'", 4.08), ("'iy'", 4.01), ("'left'", 4.01), ("'in'", 3.97)]
 complete delta, answer-query -> keys -: [("' Pelt'", -4.15), ("' Rwand'", -4.08), ("'rollup'", -4.01), ("' Rwandan'", -3.97), ("' kif'", -3.96), ("' fadeInUp'", -3.94), ("'MeshData'", -3.82)]
