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Yet most still remain unable to support natural, long-term companion-like interactions, resulting in experiences that feel episodic and inauthentic. We argue that current agents overlooked cross-temporal modeling of agents' social behaviors and internal emotions: generated behaviors rarely influence an agent's emotional state, and emotional states seldom shape subsequent behaviors. We present Cross-Temporal Emotion Modeling (CTEM), a framework that links long-term behavioral history to moment-to-moment emotional expression. CTEM establishes a closed loop where past experiences update an evolving emotional state; this state conditions immediate interactions; and user feedback continually revises both memory and emotional state, enabling reflection and anticipation. 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CTEM establishes a closed loop where past experiences update an evolving emotional state; this state conditions immediate interactions; and user feedback continually revises both memory and emotional state, enabling reflection and anticipation. 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