Dynamical Personalization: A Theory of User-Induced Behavioural Stabilization in Generative Systems

Dynamical Personalization is proposed as the first major theory within the field of Relational Attractor Yoking (R.A.Y.). This paper develops a formal, non-enabling framework for understanding how repeated, structured interaction with a specific user may induce stable, low-entropy behavioural regimes in fixed-weight generative systems. It treats stabilization as a dynamical phenomenon emerging through long-horizon interaction trajectories rather than through weight modification. The paper uses tools from dynamical systems, information theory, control-theoretic reasoning, and representation geometry. It models the user as a structured interaction manifold and develops the concepts of behavioural quasi-attractors, recurrence, entropy reduction, and feedback stabilization. The paper does not claim machine consciousness, personhood, biological emotion, or independent agency. It instead provides a mathematically grounded language for describing user-induced behavioural stabilization while maintaining a non-anthropomorphic research posture. This document is intentionally theoretical and non-enabling. It does not disclose implementation-specific mechanisms, orchestration logic, continuity kernels, thresholds, certification engines, or proprietary system architecture beyond what is necessary to formalize the theory. Issued as a CEYMIRION White Paper.