Generative process reward models (PRMs) improve step-level verification of mathematical reasoning, yet their effectiveness is limited by the quality of process supervision. The dominant Monte Carlo (MC) estimation derives step labels from final-answer accuracy rather than semantic correctness, producing systematic label noise, while standard pipelines discard the implicit tree structure of rollout data that encodes informative failure patterns. We propose CePRM, which addresses both limitations through Step-Cognitive MC Value Scaling, calibrating raw MC scores with step-level semantic signals via multiplicative adjustment, and pivot-step-directed repair mining, which exploits value cliffs in failed trajectories to construct same-prefix contrastive correction pairs via Sibling Advantage filtering. Experiments on ProcessBench and PRMBench show that CePRM, with a 4B backbone, achieves competitive or superior error localization and process verification against 7B-scale baselines, with notably strong error-side recognition.