=== POSITIONAL NUMERATOR AND NORMALIZATION GEOMETRY ===
Numerator relatives compare coefficient matrices, NOT attention scores.
Denominator relatives compare quadratic coefficient matrices.
 L H    zero     median      min       max max_lag    Qden_rel  Kden_rel
 0 0   0.01218   0.01152   0.01057   0.01237       2    0.002031   0.003332
 0 1   0.00917   0.00859   0.00828   0.00917       0    0.004127   0.003332
 0 2   0.00797   0.00717   0.00640   0.00797       0    0.002493   0.003332
 0 3   0.01039   0.00960   0.00930   0.01040       1    0.004221   0.003332
 1 0   0.00949   0.00920   0.00896   0.00965       1    0.003189   0.004947
 1 1   0.00975   0.00987   0.00961   0.01015     128    0.005050   0.004947
 1 2   0.01267   0.01241   0.01124   0.01267       0    0.001914   0.004947
 1 3   0.00975   0.00951   0.00938   0.00992       1    0.004840   0.004947
 2 0   0.01091   0.00992   0.00945   0.01115       2    0.004566   0.005603
 2 1   0.00876   0.00858   0.00839   0.00883       1    0.005500   0.005603
 2 2   0.01207   0.01113   0.01042   0.01237       2    0.003713   0.005603
 2 3   0.01443   0.01225   0.01157   0.01606       2    0.002918   0.005603
 3 0   0.00867   0.00836   0.00802   0.00868       1    0.004683   0.004431
 3 1   0.01889   0.01666   0.01477   0.01912       1    0.004024   0.004431
 3 2   0.01259   0.01162   0.01064   0.01268       1    0.004732   0.004431
 3 3   0.00652   0.00633   0.00609   0.00652       0    0.004859   0.004431
 4 0   0.01227   0.01145   0.01043   0.01300       4    0.004113   0.003662
 4 1   0.01738   0.01265   0.01078   0.01854       1    0.002811   0.003662
 4 2   0.01472   0.01299   0.01009   0.01530       2    0.002865   0.003662
 4 3   0.01318   0.01304   0.01011   0.01363       4    0.001129   0.003662
 5 0   0.02297   0.02221   0.01916   0.02299       1    0.003767   0.002664
 5 1   0.01413   0.01391   0.01368   0.01413       0    0.004835   0.002664
 5 2   0.01836   0.01806   0.01732   0.01837       8    0.005442   0.002664
 5 3   0.02461   0.02376   0.02152   0.02466       2    0.004868   0.002664
 6 0   0.01513   0.01475   0.01283   0.01513       0    0.005364   0.004081
 6 1   0.01762   0.01715   0.01411   0.01771       1    0.004786   0.004081
 6 2   0.02319   0.01979   0.01362   0.02343       1    0.003270   0.004081
 6 3   0.01629   0.01536   0.01241   0.01637       1    0.004505   0.004081
 7 0   0.01252   0.01192   0.00925   0.01256       1    0.003550   0.004432
 7 1   0.01673   0.01501   0.01198   0.01673       0    0.004038   0.004432
 7 2   0.01457   0.01413   0.01124   0.01465       8    0.003499   0.004432
 7 3   0.02052   0.01766   0.01259   0.02063       1    0.003340   0.004432
 8 0   0.01271   0.01101   0.00962   0.01271       0    0.004345   0.003946
 8 1   0.01170   0.01036   0.00933   0.01186       1    0.004377   0.003946
 8 2   0.01638   0.01344   0.01050   0.01712       2    0.003324   0.003946
 8 3   0.01356   0.01313   0.01001   0.01388       2    0.004237   0.003946
 9 0   0.01855   0.01740   0.01232   0.01856       1    0.003677   0.004604
 9 1   0.01390   0.01352   0.01066   0.01390       0    0.003674   0.004604
 9 2   0.01868   0.01699   0.01196   0.01871       1    0.003052   0.004604
 9 3   0.01244   0.01224   0.00993   0.01246       1    0.003566   0.004604
10 0   0.02253   0.02033   0.01339   0.02254       1    0.004857   0.004421
10 1   0.03276   0.02262   0.01729   0.03406       1    0.002865   0.004421
10 2   0.01035   0.01035   0.00867   0.01056      16    0.004083   0.004421
10 3   0.01781   0.01700   0.01253   0.01804       2    0.004232   0.004421
11 0   0.04659   0.03799   0.02887   0.04690       1    0.004474   0.008137
11 1   0.03806   0.03254   0.02643   0.03883       2    0.004182   0.008137
11 2   0.01811   0.01784   0.01599   0.01837      16    0.007235   0.008137
11 3   0.02737   0.02668   0.02173   0.02737       0    0.006066   0.008137
12 0   0.03024   0.03024   0.02534   0.03237       8    0.004772   0.005361
12 1   0.02387   0.02394   0.01966   0.02517      16    0.009680   0.005361
12 2   0.03113   0.03113   0.02368   0.03222      16    0.005380   0.005361
12 3   0.02583   0.02591   0.02301   0.02759      32    0.005705   0.005361
13 0   0.01688   0.01511   0.01180   0.01688       0    0.004009   0.002664
13 1   0.02173   0.01691   0.01341   0.02196       1    0.002822   0.002664
13 2   0.02365   0.01719   0.01408   0.02365       0    0.002899   0.002664
13 3   0.01200   0.01203   0.01155   0.01313      16    0.005332   0.002664
14 0   0.01740   0.01549   0.01303   0.01740       1    0.002867   0.002877
14 1   0.02586   0.02076   0.01490   0.02588       1    0.003232   0.002877
14 2   0.01792   0.01790   0.01462   0.01859      16    0.002748   0.002877
14 3   0.02001   0.01828   0.01428   0.02012       1    0.003392   0.002877
15 0   0.02271   0.01920   0.01603   0.02307       1    0.004215   0.004354
15 1   0.01459   0.01362   0.01264   0.01459       0    0.004750   0.004354
15 2   0.01881   0.01637   0.01486   0.01881       0    0.004536   0.004354
15 3   0.01336   0.01254   0.01123   0.01336       0    0.004199   0.004354
16 0   0.01464   0.01243   0.01146   0.01464       0    0.002381   0.003068
16 1   0.01664   0.01317   0.01176   0.01715       1    0.002344   0.003068
16 2   0.01601   0.01252   0.01169   0.01601       0    0.002386   0.003068
16 3   0.01167   0.01074   0.01016   0.01167       0    0.003002   0.003068
17 0   0.01554   0.01426   0.01306   0.01555       1    0.004257   0.002401
17 1   0.02298   0.01854   0.01698   0.02315       1    0.003833   0.002401
17 2   0.00890   0.00886   0.00803   0.01221    4096    0.005132   0.002401
17 3   0.01489   0.01358   0.01261   0.01489       0    0.004361   0.002401

=== TOP 15 HEADS BY MEDIAN POSITIONAL NUMERATOR DIFFERENCE ===
L11H0 full_attention    median=0.037995 zero=0.046586 Qden=0.004474 Kden=0.008137 median_identity_change_B-A=+0.0002759
L11H1 full_attention    median=0.032544 zero=0.038064 Qden=0.004182 Kden=0.008137 median_identity_change_B-A=-0.0000328
L12H2 sliding_attention median=0.031127 zero=0.031127 Qden=0.005380 Kden=0.005361 median_identity_change_B-A=+0.0002484
L12H0 sliding_attention median=0.030242 zero=0.030242 Qden=0.004772 Kden=0.005361 median_identity_change_B-A=+0.0001197
L11H3 full_attention    median=0.026676 zero=0.027372 Qden=0.006066 Kden=0.008137 median_identity_change_B-A=+0.0002073
L12H3 sliding_attention median=0.025908 zero=0.025832 Qden=0.005705 Kden=0.005361 median_identity_change_B-A=-0.0001114
L12H1 sliding_attention median=0.023941 zero=0.023867 Qden=0.009680 Kden=0.005361 median_identity_change_B-A=+0.0001018
L05H3 full_attention    median=0.023764 zero=0.024607 Qden=0.004868 Kden=0.002664 median_identity_change_B-A=+0.0001994
L10H1 sliding_attention median=0.022622 zero=0.032764 Qden=0.002865 Kden=0.004421 median_identity_change_B-A=+0.0002260
L05H0 full_attention    median=0.022206 zero=0.022973 Qden=0.003767 Kden=0.002664 median_identity_change_B-A=+0.0000979
L14H1 sliding_attention median=0.020764 zero=0.025863 Qden=0.003232 Kden=0.002877 median_identity_change_B-A=+0.0000619
L10H0 sliding_attention median=0.020332 zero=0.022533 Qden=0.004857 Kden=0.004421 median_identity_change_B-A=+0.0000049
L06H2 sliding_attention median=0.019793 zero=0.023186 Qden=0.003270 Kden=0.004081 median_identity_change_B-A=-0.0000742
L15H0 sliding_attention median=0.019202 zero=0.022712 Qden=0.004215 Kden=0.004354 median_identity_change_B-A=+0.0000666
L17H1 full_attention    median=0.018541 zero=0.022978 Qden=0.003833 Kden=0.002401 median_identity_change_B-A=+0.0002476

=== POSITION PROFILES FOR TOP SIX HEADS ===
L11H0: 0:0.04659, 1:0.04690, 2:0.04670, 4:0.04553, 8:0.04446, 16:0.04242, 32:0.04161, 64:0.03799, 128:0.03466, 256:0.03233, 511:0.03162, 512:0.03150, 1024:0.02920, 2048:0.02887, 4096:0.02974
L11H1: 0:0.03806, 1:0.03867, 2:0.03883, 4:0.03819, 8:0.03683, 16:0.03636, 32:0.03420, 64:0.03254, 128:0.03191, 256:0.03159, 511:0.02976, 512:0.02988, 1024:0.02689, 2048:0.02643, 4096:0.02658
L12H2: 0:0.03113, 1:0.03127, 2:0.03137, 4:0.03144, 8:0.03194, 16:0.03222, 32:0.02954, 64:0.02655, 128:0.02566, 256:0.02368, 511:0.02395
L12H0: 0:0.03024, 1:0.03049, 2:0.03069, 4:0.03097, 8:0.03237, 16:0.03145, 32:0.02859, 64:0.02657, 128:0.02758, 256:0.02611, 511:0.02534
L11H3: 0:0.02737, 1:0.02735, 2:0.02735, 4:0.02726, 8:0.02713, 16:0.02701, 32:0.02696, 64:0.02668, 128:0.02588, 256:0.02488, 511:0.02449, 512:0.02448, 1024:0.02368, 2048:0.02179, 4096:0.02173
L12H3: 0:0.02583, 1:0.02589, 2:0.02594, 4:0.02606, 8:0.02696, 16:0.02747, 32:0.02759, 64:0.02537, 128:0.02591, 256:0.02320, 511:0.02301

=== TOP TEN QUERY-NORMALIZATION GEOMETRY DIFFERENCES ===
L12H1 Qden_relative=0.009680 numerator_median=0.023941
L11H2 Qden_relative=0.007235 numerator_median=0.017844
L11H3 Qden_relative=0.006066 numerator_median=0.026676
L12H3 Qden_relative=0.005705 numerator_median=0.025908
L02H1 Qden_relative=0.005500 numerator_median=0.008583
L05H2 Qden_relative=0.005442 numerator_median=0.018057
L12H2 Qden_relative=0.005380 numerator_median=0.031127
L06H0 Qden_relative=0.005364 numerator_median=0.014750
L13H3 Qden_relative=0.005332 numerator_median=0.012034
L17H2 Qden_relative=0.005132 numerator_median=0.008859

Canonical denominator isotropic-floor coefficient range: (4.1098401554055006e-13, 6.155595887300753e-11)
Canonical denominator constant coefficient range: (2.630297699459521e-16, 3.939581367872482e-14)

Interpretation limits:
These coefficients specify aspects of how matching depends on residual
coordinates and relative position, but they have not been evaluated.
A small coefficient can still matter on an unknown, nearly null direction.
No hidden states, RMS values of states, attention scores, softmax,
logits, probabilities, or model outputs were computed.
