Chain-of-Thought (CoT) reasoning has significantly enhanced the reasoning capabilities of large language models (LLMs). However, existing reinforcement learning methods primarily optimize outcome-level rewards, providing limited supervision over the reasoning process. As a result, models may produce shortcut-prone or unstable reasoning trajectories even when the final answer is correct. We propose GeoFaith, a spatio-temporal latent dynamics framework for learning faithful reasoning processes without process reward models. GeoFaith combines final-state latent uncertainty, which measures whether a completed trajectory lies in a well-supported manifold region, with predictive-entropy dynamics, which penalize abnormal uncertainty patterns such as premature collapse, oscillation, and prolonged uncertainty. These signals are incorporated as process regularization into GRPO, jointly optimizing answer correctness and reasoning quality without step-level process annotations. Experiments show that GeoFaith consistently improves reasoning accuracy, produces more efficient reasoning trajectories, and outperforms both outcome-only reinforcement learning and process-supervision baselines.

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