# Cross-format error-awareness transfer — rigorous summary

Model: Qwen/Qwen2.5-7B-Instruct
Features: top-50 tokens by |Cohen's d| on arithmetic train; logistic regression.
Bootstrap: 2000 resamples, percentile 95% CI, seed 42.

## IN-FORMAT (held-out arithmetic test, 20%)
  AUC-ROC = 0.9683  (95% CI 0.9352-0.9928, n=120)

## CROSS-FORMAT (all capital-city statements)
  AUC-ROC = 0.6490  (95% CI 0.5834-0.7075, n=300)

## Transfer gap
  in-format minus cross-format AUC = +0.3194

## Secondary diagnostics
  capitals-internal AUC (5-fold OOF within capitals) = 0.9905 (95% CI 0.9796-0.9980, n=300)
  mean P('.')  arithmetic: correct=0.921  incorrect=0.567  (gap=+0.354)
  mean P('.')  capitals:   correct=0.971  incorrect=0.986  (gap=-0.014)

## Verdict
  The arithmetic-trained error-awareness classifier transfers only partially to capital-city statements: cross-format AUC is above chance but well below in-format, so the signal is part shared, part format-specific.