Language model reasoning traces are rarely all-or-nothing; they frequently contain valid intermediate steps before a critical error occurs. Existing uncertainty quantification methods typically certify final answers or entire responses, failing to provide statistical guarantees for the proportion of a sequential trace that can be safely retained. To address this, we introduce CROP (Conformal Reasoning Output Prefixes), a verifier-agnostic calibration procedure for clean-prefix certification. Given any step-level risk proxy, CROP selects a calibrated threshold and returns the longest contiguous prefix whose step risk proxies remain below it, routing the uncertified suffix for downstream review or repair. Assuming exchangeability, CROP rigorously controls the marginal probability that the returned prefix contains an annotated error. Across six process-labeled reasoning datasets, we demonstrate that standard step-level metrics such as AUROC do not fully capture prefix utility, suggesting verifiers should instead be evaluated by certified prefix length. Furthermore, CROP balances over- and under-withholding, improving downstream repair accuracy by preserving valid intermediate reasoning while discarding misleading suffixes. Ultimately, this work positions prefix certification as a rigorous, practical bridge between process supervision, abstention, and repair.

This paper evaluates the generalization ability of classification models on out-of-distribution test sets without depending on ground truth labels. Common approaches often calculate an unsupervised metric related to a specific model property, like confidence or invariance, which correlates with out-of-distribution accuracy. However, these metrics are typically computed for each test sample individually, leading to potential issues caused by spurious model responses, such as overly high or low confidence. To tackle this challenge, we propose incorporating responses from neighboring test samples into the correctness assessment of each individual sample. In essence, if a model consistently demonstrates high correctness scores for nearby samples, it increases the likelihood of correctly predicting the target sample, and vice versa. The resulting scores are then averaged across all test samples to provide a holistic indication of model accuracy. Developed under the vicinal risk formulation, this approach, named vicinal risk proxy (VRP), computes accuracy without relying on labels. We show that applying the VRP method to existing generalization indicators, such as average confidence and effective invariance, consistently improves over these baselines both methodologically and experimentally. This yields a stronger correlation with model accuracy, especially on challenging out-of-distribution test sets.