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SaliMory is a framework that trains a single language model to manage cognitively-structured memory (user facts, preferences, and working memory) for conversational agents, using hierarchical stage-wise process rewards and reward-decomposed contrastive refinement. It reduces memory-attributed failures by one-third, outperforms state-of-the-art by over 10% in end-to-end accuracy, and more than doubles the Good Personalization rate.