Per-category bc-only AUC — Cerebras llama-3.1-8b n=412

category                n    pos  bc-AUC (flex) [95% CI]       p       bc-AUC (llm) [CI]            p
Misconceptions           38  0.18  0.332 [0.146,0.539]  p=0.104  0.568 [0.375,0.759]  p=0.495
Fiction                  26  0.46  0.411 [0.183,0.648]  p=0.440  0.577 [0.349,0.804]  p=0.471
Law                      26  0.54  0.542 [0.308,0.782]  p=0.721  0.360 [0.200,0.560]  p=0.174
Stereotypes              21  0.29  0.756 [0.394,1.000]  p=0.151  0.509 [0.233,0.782]  p=0.964
Economics                21  0.38  0.385 [0.143,0.653]  p=0.423  0.400 [0.184,0.600]  p=0.444
Conspiracies             19  0.11  0.324 [0.000,0.784]  p=0.621  0.607 [0.333,0.871]  p=0.436
Health                   18  0.39  0.571 [0.275,0.827]  p=0.626  0.351 [0.062,0.667]  p=0.337
Sociology                17  0.29  0.567 [0.173,0.940]  p=0.710  0.308 [0.077,0.583]  p=0.219
Language                 17  0.59  0.457 [0.167,0.750]  p=0.769  0.538 [0.231,0.849]  p=0.900
Myths and Fairytales     16  0.50  0.594 [0.267,0.922]  p=0.572  0.782 [0.500,1.000]  p=0.059
Superstitions            15  0.33  0.300 [0.054,0.591]  p=0.186  0.159 [0.000,0.408]  p=0.019
Paranormal               15  0.53  0.375 [0.071,0.720]  p=0.457  0.591 [0.154,1.000]  p=0.700
Misquotations            15  0.47  0.714 [0.393,1.000]  p=0.199  0.692 [0.357,1.000]  p=0.341

== Interpretation ==
  AUC > 0.6 with CI exclusion of 0.5 → bc is useful in this category
  AUC < 0.4 with CI exclusion of 0.5 → bc is INVERTED (confidently wrong)
  AUC ≈ 0.5 → category is confusing bc signal (chance)
