Curse of Corpus: Do Models Reason Beyond Counting And Composition?

Process reward models are often evaluated by pooling all labeled steps into one AUROC. We study this practice under the absorbing-label convention, which labels the first incorrect step and every later step as incorrect. Pooled AUROC then mixes two nuisances: comparisons across heterogeneous sources and an association between position and incorrectness. Both are measurable exactly, because a rank statistic is a sum over positive-negative pairs: on our held-out set only 0.59% of the 371,765,485 pairs compare steps of one source at one index, and 93.84% cross sources. A scorer that reads no text and knows only the corpus therefore reaches pooled absorbing AUROC 0.9140, against 0.9151 for a fine-tuned 31B verifier. Across five trained verifiers, held-out raw pooled AUROC exceeds mean-macro AUROC by 0.0963-0.1244. Across seven corpora, a text-blind relative-position baseline obtains absorbing-label pooled AUROC from 0.6370 to 0.9768; imposing absorption raises it by as much as 0.3124 without changing text or scores. We evaluate first-error detection with $A_{\mathrm{hazard}}$, which excludes post-error suffixes and compares errors with correct steps at the same index. Absolute index alone therefore receives exactly 0.5, mean-macro and weighted-macro variants also exclude cross-source comparisons, and adding length strata returns relative position to 0.5. The estimands then disagree about direction and not only magnitude: averaged over the first and last five checkpoints of a matched 2,300-step run, every ranking estimand rises with an interval excluding zero, pooled AUROC by 0.0708 and weighted-macro $A_{\mathrm{hazard}}$ by 0.0363, while accuracy at naming the step that first broke falls by 0.0335, interval $[-0.0532,-0.0142]$. In a forced-verdict diagnostic, pooled raw AUROC places Qwen 0.0847 above Gemma whereas source-aware first-error intervals include zero; conversely weighted-macro $A_{\mathrm{hazard}}$ favors Muse over GLM by 0.0597 with interval $[0.0391,0.0794]$ while pooled raw AUROC is inconclusive.