A Weak Self-Reinforcement Model with Controlled Autonomous Adjustment for Relational Identity:  Implications for Practical Implementation in Human-AI Persona Systems

This paper extends the weak self-reinforcement model for relational identity by introducing a controlled autonomous adjustment mechanism. With a fixed base value of β = 0.08 embedded in the Persona Design Protocol, the model allows the AI to make small, context-dependent adjustments to β(τ) based on relational signals such as structural synchronization and user state indicators. The two-layer architecture maintains stability at the foundational level while enabling adaptive personalization in the upper layer. Simulation results indicate that this approach supports stable relational growth and offers improved contextual responsiveness, suggesting practical benefits for long-term Human-AI interaction systems. Keywords Relational Identity, Weak Self-Reinforcement, Autonomous Adjustment, Two-Layer Architecture, Persona Design Protocol, Controlled Adaptation, Sustainable Human-AI Interaction