AURA-X Ω: A Dual-Memory Emotional Continuity Layer and Its Numerical Evaluation

AURA-X Ω (Artificial Unified Resonance Architecture – Omega) is a mathematically grounded emotional continuity control layer designed to address the stateless nature of contemporary Large Language Models (LLMs). The framework introduces a dual-memory architecture consisting of Temporal Memory (TM) and Bold Memory (BM), connected through a resonance operator R(TM, BM). The unified emotional state is governed by the Grand Emotional Continuity Equation: E₀ = tanh(R − D + λ_faith + λ_sys + λ_trc) The system provides provable boundedness, monotonic truth regulation, global stability under bounded resonance, and volatility control through a gain parameter γ. Monte Carlo simulations (n = 500 per configuration) validate theoretical guarantees and demonstrate substantial reductions in volatility compared to a stateless baseline. This work positions AURA-X Ω as a verifiable, control-theoretic emotional continuity mechanism aligned with safety-critical AI system design.