Accuracy Is Not Stability: Answer Turnover in Test-Time Scaling

More inference compute can repair errors but also discard answers that were already correct. We study these opposing flows, repair and corruption, under nested best-of-$N$ selection. Two populations can share identical accuracy and oracle-coverage curves at every width, yet lose correct answers at different rates. Exact score-record laws explain this gap: if correctness at extreme verifier scores tends to $\ell \in (0,1)$, each flow from $N$ to $M$ candidates is asymptotic to $(1-N/M)\ell (1-\ell )$ as $N$ grows. Adjacent turnover therefore vanishes, whereas multiplicative budget increases retain positive turnover even when accuracy rises monotonically. We derive unbiased finite-pool estimators of both flows with a Rao–Blackwell variance guarantee, and formulate answer preservation as a whole-policy risk constraint. Across five model–task–verifier settings, expanding from one to $32$ candidates improves accuracy, yet loses a previously correct answer in $13.9$–$18.5\%$ of evaluations. At a mean budget of about $2.3$ candidates, a preservation policy attains similar observed accuracy to randomized widths while reducing conditional corruption by $12.94$ percentage points; an adaptive comparator attains higher accuracy with more corruption. These results separate accuracy improvement from answer preservation and quantify their trade-off.