PRESCALE: Exact Risk Accounting for Frozen-Bank Verifier Search

Verifier-guided Best-of-N search can improve a proxy score while replacing an incumbent with a target-worse candidate. We study this risk through offline auditing of a frozen labeled candidate bank, with target labels hidden from the selector. PRESCALE exactly integrates harmful replacement over uniform subsets sampled without replacement, including competition between harmful and benign winners. A complete score-gap vector yields a conditional risk curve without a Gaussian assumption; independent complete vectors from a specified observation law additionally support finite-sample budget calibration. Candidate-wise verifier reliability does not identify this curve. Matched-margin quadratic-Gaussian controls isolate dependence effects. On one simulated PDE trajectory, aligned score gaps yield forecast MAE of 1.11 percentage points, versus 19.68 after column shuffling preserves empirical marginals; same-information subset Monte Carlo yields 1.15.In a controlled matched-data comparison, direct-loss calibration admits budget 16 versus 4 for a marginal union-bound reduction; known Gaussian marginals also admit 16. This comparison includes union-bound slack. On MATH-500, the rank interface quantifies harmful replacements alongside accuracy gains and separates cross-bank forecast discrepancies from within-bank sampling effects. This operational audit does not establish a distinct answer-selection advantage. PRESCALE makes frozen-bank search risk computable while separating exact conditional accounting, dependence-sensitive estimation, and statistical calibration.