A Dual-Memory Framework for Ensuring Emotional Continuity in Artificial Intelligence Systems with Numerical Evaluation

This preprint introduces AURA-X Ω (Artificial Unified Resonance Architecture – Omega), a dual-memory framework designed to address the problem of emotional discontinuity in contemporary large language models (LLMs). Current LLM-based systems operate largely as stateless or short-context engines, resulting in emotionally reactive but historically incoherent behavior. The proposed architecture models emotion as a resonance process between Temporary Memory (TM), representing the immediate conversational context, and Bold Memory (BM), representing emotionally salient long-term history. This interaction is formalized through a bounded mathematical control equation that incorporates a decay term and three stabilization coefficients: belief/values (λ_faith), system constraints (λ_sys), and truth-resonance (λ_trc). A numerical evaluation and scenario-based qualitative analysis demonstrate how AURA-X Ω produces continuity-aware, safety-aligned, and identity-consistent emotional trajectories, in contrast to baseline stateless LLM behavior. The framework is implemented in an offline prototype and is intended as a middleware control layer rather than a claim of artificial consciousness. This work contributes to affective computing, AI safety, and long-term human–AI interaction design.