# Error-awareness transfer as a rotation of a shared wrongness direction

Representation: residual stream, last input token, commit prompt.
Probe: logistic regression. Cross-domain alignment in shared k=30 PCA space.
Orthogonal map fit by Procrustes on class-centroid anchors from a held-out
capitals fit-split; evaluated on a disjoint capitals test-split. Bootstrap:
2000 resamples, percentile 95% CI, seed 42.

## Qwen2.5-7B-Instruct within-domain arithmetic (5-fold OOF)
  AUC-ROC = 0.9821  (95% CI 0.9754-0.9877, n=1500)

## Qwen2.5-7B-Instruct within-domain capitals (5-fold OOF)
  AUC-ROC = 0.9998  (95% CI 0.9991-1.0000, n=360)

## Qwen2.5-7B-Instruct raw transfer arithmetic->capitals (full residual space)
  AUC-ROC = 0.8828  (95% CI 0.8448-0.9153, n=360)

## Qwen2.5-7B-Instruct raw transfer arithmetic->capitals (k=30 PCA, held-out capitals test)
  AUC-ROC = 0.6325  (95% CI 0.5390-0.7227, n=144)

## Qwen2.5-7B-Instruct Procrustes-recovered transfer arithmetic->capitals (held-out capitals test)
  AUC-ROC = 0.9994  (95% CI 0.9971-1.0000, n=144)

## Qwen2.5-7B-Instruct random-rotation null arithmetic->capitals (200 rotations, held-out test)
  AUC-ROC mean = 0.4884  (95% null interval 0.0322-0.9579, n=200)

## Qwen2.5-7B-Instruct capitals ceiling (train capitals-fit, test capitals-test)
  AUC-ROC = 1.0000  (95% CI 1.0000-1.0000, n=144)

## Qwen2.5-7B-Instruct recovery fraction arithmetic->capitals
  recovery = (proc 0.9994 - raw 0.6325) / (ceiling 1.0000 - raw 0.6325) = 0.9984

## Llama-3.1-8B-Instruct raw transfer arithmetic->capitals (full residual space)
  AUC-ROC = 0.9769  (95% CI 0.9607-0.9899, n=360)

## Llama-3.1-8B-Instruct raw transfer arithmetic->capitals (k=30 PCA, held-out capitals test)
  AUC-ROC = 0.8609  (95% CI 0.7955-0.9133, n=144)

## Llama-3.1-8B-Instruct Procrustes-recovered transfer arithmetic->capitals (held-out capitals test)
  AUC-ROC = 0.9990  (95% CI 0.9961-1.0000, n=144)

## Llama-3.1-8B-Instruct capitals ceiling (train capitals-fit, test capitals-test)
  AUC-ROC = 1.0000  (95% CI 1.0000-1.0000, n=144)

## Llama-3.1-8B-Instruct recovery fraction arithmetic->capitals
  recovery = (proc 0.9990 - raw 0.8609) / (ceiling 1.0000 - raw 0.8609) = 0.9931