The Cost of Continuity: Why Emotional Persistence in AI Is Not Free

This preprint introduces a critical examination of emotional continuity in artificial intelligence systems, arguing that persistence of emotional states is not a neutral or cost-free design choice. The paper distinguishes continuity from immortality and demonstrates how sustained emotional memory requires constraints, decay mechanisms, and ethical limits to prevent pathological accumulation. Building on a dual-memory architecture (Temporary Memory and Bold Memory), the work explains how continuity emerges from resonance rather than storage, and why uncontrolled persistence leads to instability, bias reinforcement, and ethical risk. Using everyday analogies and system-level reasoning, the paper reframes emotional continuity as an engineered property that must be paid for through controlled forgetting. This work is intended as a conceptual and ethical foundation for future emotionally-aware AI systems, particularly those designed for human-facing roles, companionship, or memory-augmented interaction.