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LLM agents are increasingly used for social simulation, yet emotion is often treated as a transient cue, causing emotional amnesia and weak long-horizon continuity. We present Sentipolis, a framework for emotionally stateful agents that integrates continuous Pleasure-Arousal-Dominance (PAD) representation, dual-speed emotion dynamics, and emotion--memory coupling. Across thousands of interactions over multiple base models and evaluators, Sentipolis improves emotionally grounded behavior, boosting communication, and emotional continuity. Gains are model-dependent: believability increases for higher-capacity models but can drop for smaller ones, and emotion-awareness can mildly reduce adherence to social norms, reflecting a human-like tension between emotion-driven behavior and rule compliance in social simulation. Network-level diagnostics show reciprocal, moderately clustered, and temporally stable relationship structures, supporting the study of cumulative social dynamics such as alliance formation and gradual relationship change.