AURA-X Ω: A Dual-Memory Emotional Continuity Layer for Large Language Models

Large Language Models (LLMs) exhibit emotional amnesia due to their stateless interaction design, causing loss of continuity across conversations. This work introduces AURA-X Ω, a dual-memory emotional continuity layer composed of Temporal Memory (TM) and Bold Memory (BM). TM stores short-term conversational context while BM retains emotionally significant events with controlled decay dynamics. The interaction between these memory layers generates an emotional state through a bounded resonance function that stabilizes chatbot behavior over time. The framework introduces a mathematical formulation for emotional continuity, resonance dynamics, and bounded volatility in AI systems. A lightweight prototype implementation demonstrates the feasibility of integrating the architecture into conversational agents. AURA-X Ω aims to improve long-term emotional coherence, stability, and relational continuity in AI companions, therapeutic chatbots, and human-AI interaction systems.