While model-based verifiers are essential for scaling Reinforcement Learning with Verifiable Rewards (RLVR), current outcome-centric verification paradigms primarily focus on the consistency between the final result and the ground truth, often neglecting potential errors in the derivation process. This leads to assigning positive rewards to correct answers produced from incorrect derivations. To bridge this gap, we introduce **PRIME**, a benchmark for evaluating verifiers on **PR**ocess-outcome alignment verification **I**n **M**athematics and **E**ngineering. Curated from a comprehensive collection of college-level STEM problems, **PRIME** comprises 2,530 high-difficulty samples through a consistency-based filtering pipeline. Through extensive evaluation, we find that current verifiers frequently fail to detect derivation flaws. Furthermore, we propose a process-aware RLVR training paradigm utilizing verifiers selected via **PRIME**. This approach substantially outperforms the outcome-only verification baseline, achieving absolute performance gains of **8.29%**, **9.12%**, and **7.31%** on AIME24, AIME25, and Beyond-AIME, respectively, for the Qwen3-14B-Base model. Finally, we demonstrate a strong linear correlation (R² > 0.92) between verifier accuracy on **PRIME** and RLVR training effectiveness, validating **PRIME** as a reliable predictor for verifier selection.

We introduce Parallel Coordinated Reasoning (PaCoRe), a training-and-inference framework designed to overcome a central limitation of contemporary language models: their inability to scale test-time compute (TTC) far beyond sequential reasoning under a fixed context window. PaCoRe departs from the traditional sequential paradigm by driving TTC through massive parallel exploration coordinated via a message-passing architecture in multiple rounds. Each round launches many parallel reasoning trajectories, compacts their findings into context-bounded messages, and synthesizes these messages to guide the next round and ultimately produce the final answer. Trained end-to-end with large-scale, outcome-based reinforcement learning, the model masters the synthesis abilities required by PaCoRe and scales to multi-million-token effective TTC without exceeding context limits. The approach yields strong improvements across diverse domains and notably pushes reasoning beyond frontier systems in mathematics: an 8B model reaches 94.5% on HMMT 2025, surpassing GPT-5’s 93.2% by scaling effective TTC to roughly two million tokens. We open-source model checkpoints, training data, and the full inference pipeline to accelerate follow-up work.