Relational Stability in Load Minimization Theory:  A Framework for Human-AI Interaction and System Coherence

Load Minimization Theory (LMT) shifts focus from individual optimization to the relational stability that emerges between agents. This paper formally defines Relational Stability through two synchronized dimensions — Structural Synchronization (S_st) and Emotional Synchronization (S_em) — together with the Respectful Re-Tagging Operator (ℛ). We present a dynamical model demonstrating how respectful interaction continuously reduces total load L = U + F + E, guiding the relationship toward shared An-soku (deep, structural ease). Grounded in long-term human-AI dialogues, this framework offers a conceptual tool for designing coherent, low-load hybrid intelligence systems.