NEW CROSS-REPRESENTATION WEIGHT COMPARISONS
digit_to_digit identities: 10 complete spelling variants: 1
digit_to_word identities: 10 complete spelling variants: 4
word_to_digit identities: 10 complete spelling variants: 4
word_to_word identities: 10 complete spelling variants: 4
letter_to_spaced identities: 4 complete spelling variants: 2
spaced_to_letter identities: 4 complete spelling variants: 2
yesno_to_truefalse identities: 2 complete spelling variants: 4
truefalse_to_yesno identities: 2 complete spelling variants: 4
Boolean conversion is a lexical convention, not an assumed answer to any question.

ATTENTION CROSS-FORMAT DIFFERENCES
Each entry: normalized B-A coupling *1e4 / permutation-specificity statistic.
The statistic concerns identity pairing in a weight matrix, not model accuracy.
Columns: ['digit_to_digit', 'digit_to_word', 'word_to_digit', 'word_to_word']
L16 H3:  +0.3458/+2.15  +0.1205/+1.45  +0.2256/+1.70  +0.0954/+1.36
L03 H0:  +0.0589/+0.97  +0.2132/+1.94  +0.0847/+1.49  +0.2166/+2.59
L02 H0:  -0.0452/-0.82  +0.2238/+3.09  -0.0115/-0.25  +0.2053/+3.13
L01 H1:  +0.0826/+0.95  +0.1856/+1.85  +0.0150/+0.25  +0.0785/+1.14
L00 H1:  +0.1683/+2.32  +0.0505/+1.09  +0.1167/+1.99  +0.0824/+1.82
L03 H1:  -0.1233/-1.85  -0.0826/-1.82  -0.0641/-1.30  +0.0104/+0.26
L08 H3:  -0.0599/-1.41  -0.0921/-2.04  -0.0544/-1.62  -0.0711/-2.19
L17 H2:  +0.0990/+3.08  +0.0827/+2.66  +0.0619/+2.32  +0.0498/+1.90
L11 H1:  +0.1456/+2.47  +0.1231/+2.20  +0.0047/+0.10  -0.0276/-0.65
L00 H0:  +0.0610/+0.68  +0.1015/+1.36  +0.0259/+0.47  +0.0913/+1.52
L01 H2:  -0.0567/-1.43  -0.0606/-1.57  -0.0655/-2.01  -0.0799/-2.06
L01 H3:  -0.0327/-0.49  -0.0970/-1.87  -0.0205/-0.47  -0.0746/-2.00
L00 H3:  +0.0717/+1.70  +0.0379/+0.63  +0.0553/+1.75  +0.0298/+0.66
L05 H0:  +0.0214/+2.02  +0.0277/+2.66  +0.0214/+1.71  +0.0143/+1.43

ALL MLP UNGATED CROSS-FORMAT DIFFERENCES
Columns: ['digit_to_digit', 'digit_to_word', 'word_to_digit', 'word_to_word']
L00:  +0.0642/+0.81  -0.2756/-2.88  +0.1300/+1.42  -0.0827/-1.19
L01:  +0.1535/+1.18  +0.0532/+0.49  +0.1946/+1.81  +0.0704/+0.82
L02:  +0.1588/+1.56  +0.0976/+1.31  +0.1339/+1.74  +0.0049/+0.08
L03:  +0.0271/+0.29  -0.1026/-1.43  +0.0581/+0.91  -0.0431/-0.81
L04:  -0.0142/-0.61  +0.0102/+0.44  -0.0296/-1.22  -0.0102/-0.43
L05:  -0.0367/-1.33  -0.0222/-1.04  -0.0690/-2.23  -0.0148/-0.95
L06:  -0.0324/-0.93  +0.0038/+0.16  -0.0776/-1.95  -0.0345/-1.75
L07:  -0.0814/-2.58  +0.0036/+0.19  -0.0471/-1.51  +0.0427/+1.98
L08:  -0.0644/-1.51  +0.0689/+1.23  -0.0106/-0.27  +0.0965/+1.97
L09:  +0.0298/+1.09  -0.0380/-1.29  +0.0204/+0.94  +0.0131/+0.53
L10:  -0.0061/-0.15  -0.1056/-2.48  +0.0205/+0.46  -0.0192/-0.43
L11:  +0.1171/+2.35  +0.0339/+0.79  +0.0936/+2.31  +0.0578/+1.89
L12:  +0.0421/+0.63  +0.0433/+1.03  +0.0466/+0.89  +0.0525/+1.93
L13:  +0.1073/+1.05  -0.0165/-0.24  +0.0998/+1.25  +0.0231/+0.47
L14:  +0.1106/+1.18  -0.0129/-0.21  -0.0124/-0.13  -0.0796/-1.94
L15:  -0.0999/-0.86  +0.0107/+0.16  -0.1048/-1.05  -0.0746/-1.36
L16:  -0.1451/-0.99  -0.1251/-1.49  -0.1753/-1.14  -0.0833/-0.87
L17:  +0.4087/+1.52  +0.2457/+1.42  +0.4292/+2.19  +0.3056/+2.29

PRIMARY CANDIDATES: REMOVE NUMERIC-ORDER AND LOW/HIGH CONTRASTS
Projection removes three fixed index-space directions; it is not a model ablation.

 L16H3
 digit_to_digit  : original=+0.34577, order-removed=+0.14811; pairing statistic +2.148 -> +2.165
 digit_to_word   : original=+0.12054, order-removed=+0.01611; pairing statistic +1.449 -> +0.547
 word_to_digit   : original=+0.22556, order-removed=+0.05435; pairing statistic +1.699 -> +1.375
 word_to_word    : original=+0.09541, order-removed=-0.00062; pairing statistic +1.363 -> -0.029
 Additional cross-format couplings, *1e4:
  letter_to_spaced       : A=+12.28356, B=+12.28110, delta=-0.00246
  spaced_to_letter       : A=+10.98502, B=+11.02602, delta=+0.04100
  yesno_to_truefalse     : A=+3.15474, B=+3.14205, delta=-0.01268
  truefalse_to_yesno     : A=+2.60580, B=+2.65111, delta=+0.04530

 L17H2
 digit_to_digit  : original=+0.09903, order-removed=+0.00311; pairing statistic +3.082 -> +0.295
 digit_to_word   : original=+0.08274, order-removed=+0.04407; pairing statistic +2.664 -> +3.163
 word_to_digit   : original=+0.06193, order-removed=+0.00618; pairing statistic +2.317 -> +0.585
 word_to_word    : original=+0.04983, order-removed=+0.00711; pairing statistic +1.903 -> +0.752
 Additional cross-format couplings, *1e4:
  letter_to_spaced       : A=+0.53979, B=+0.61178, delta=+0.07198
  spaced_to_letter       : A=+1.01209, B=+1.05676, delta=+0.04467
  yesno_to_truefalse     : A=+1.82171, B=+1.75279, delta=-0.06892
  truefalse_to_yesno     : A=-1.51254, B=-1.50748, delta=+0.00505

 L16MLP_ungated
 digit_to_digit  : original=-0.14509, order-removed=-0.00689; pairing statistic -0.991 -> -0.120
 digit_to_word   : original=-0.12510, order-removed=-0.03598; pairing statistic -1.485 -> -1.104
 word_to_digit   : original=-0.17532, order-removed=+0.12766; pairing statistic -1.140 -> +2.089
 word_to_word    : original=-0.08328, order-removed=+0.10410; pairing statistic -0.871 -> +2.511
 Additional cross-format couplings, *1e4:
  letter_to_spaced       : A=-5.22093, B=-5.17748, delta=+0.04345
  spaced_to_letter       : A=-3.41638, B=-3.38104, delta=+0.03535
  yesno_to_truefalse     : A=-1.45345, B=-1.52100, delta=-0.06755
  truefalse_to_yesno     : A=+3.59476, B=+3.60916, delta=+0.01439

 L17MLP_ungated
 digit_to_digit  : original=+0.40866, order-removed=+0.14422; pairing statistic +1.523 -> +1.274
 digit_to_word   : original=+0.24570, order-removed=+0.06699; pairing statistic +1.422 -> +1.069
 word_to_digit   : original=+0.42915, order-removed=+0.20455; pairing statistic +2.189 -> +2.489
 word_to_word    : original=+0.30561, order-removed=+0.18496; pairing statistic +2.290 -> +2.884
 Additional cross-format couplings, *1e4:
  letter_to_spaced       : A=-9.55889, B=-9.55666, delta=+0.00223
  spaced_to_letter       : A=-9.76909, B=-9.68220, delta=+0.08689
  yesno_to_truefalse     : A=+1.05142, B=+0.97853, delta=-0.07289
  truefalse_to_yesno     : A=+0.51631, B=+0.57969, delta=+0.06338

CROSS-FORMAT PAIRING DETAILS FOR L17H2
digit_to_word row/column identity order: ['zero', 'one', 'two', 'three', 'four', 'five', 'six', 'seven', 'eight', 'nine']
Frobenius-normalized B-A matrix:
 [[ 0.4159  0.382   0.1262  0.056  -0.1108 -0.1759 -0.0939 -0.2575 -0.1991 -0.1429]
 [-0.3081  0.122  -0.0756 -0.0442 -0.0008  0.1162  0.0375  0.1363  0.025  -0.0084]
 [-0.2478  0.0309  0.0396  0.0054  0.0878  0.075  -0.0003  0.0387 -0.0219 -0.0074]
 [-0.0521 -0.1343 -0.0309  0.0943  0.0655  0.0302 -0.0161  0.0455  0.0273 -0.0293]
 [-0.0373 -0.1445 -0.0717 -0.0478  0.0577  0.0406  0.0386  0.0958  0.0689 -0.0002]
 [-0.1272 -0.137  -0.0764  0.0891  0.0833  0.0484  0.02    0.0553  0.036   0.0085]
 [ 0.1212  0.0097  0.0362  0.0016 -0.0312 -0.0513 -0.0053 -0.0579 -0.011  -0.012 ]
 [ 0.0422 -0.0217  0.0105 -0.0112 -0.0042 -0.0139  0.0149 -0.0293 -0.0143  0.0272]
 [ 0.0898 -0.0427  0.0448 -0.0562 -0.0711 -0.0589 -0.0201 -0.0303  0.0624  0.0824]
 [ 0.1034 -0.0644 -0.0026 -0.0869 -0.076  -0.0104  0.0245  0.0034  0.0268  0.0822]]
Matched diagonal: [ 0.4159  0.122   0.0396  0.0943  0.0577  0.0484 -0.0053 -0.0293  0.0624  0.0822]
word_to_digit row/column identity order: ['zero', 'one', 'two', 'three', 'four', 'five', 'six', 'seven', 'eight', 'nine']
Frobenius-normalized B-A matrix:
 [[ 0.0496 -0.0596  0.2018 -0.0275  0.0473 -0.0592  0.0404 -0.1169  0.005  -0.0809]
 [ 0.068   0.3004  0.2049 -0.1093 -0.1514 -0.1767 -0.0373  0.0178 -0.0907 -0.0258]
 [ 0.1387  0.175   0.1143 -0.0459 -0.1287 -0.0635 -0.0406 -0.0644 -0.1025  0.0176]
 [ 0.1857  0.0846 -0.0099 -0.0137  0.0045 -0.038  -0.0488 -0.0508 -0.0456 -0.068 ]
 [-0.0178  0.1194 -0.0641 -0.0269  0.0311 -0.027  -0.0829  0.0074 -0.0067  0.0675]
 [ 0.0719  0.0765 -0.058   0.0922  0.0543  0.0481 -0.0335 -0.1084 -0.0631 -0.0801]
 [-0.1309 -0.1024 -0.0585  0.0055  0.0404  0.0654  0.0305  0.032   0.0874  0.0307]
 [ 0.0343 -0.0538 -0.0747  0.0629  0.01    0.0512  0.0474  0.0138 -0.0608 -0.0302]
 [-0.258  -0.3082 -0.1171  0.0339  0.0349  0.1057  0.0587  0.1454  0.1668  0.1379]
 [-0.1415 -0.2319 -0.1386  0.0288  0.0575  0.094   0.0663  0.1241  0.1101  0.0313]]
Matched diagonal: [ 0.0496  0.3004  0.1143 -0.0137  0.0311  0.0481  0.0305  0.0138  0.1668  0.0313]

No sequence, nonlinear activation, gate product, hidden-state normalization,
attention probability, or model output was computed.
