Processual Identity Law: Identity Drift as a Generic Property of Dynamical Inferential Systems

This article establishes a formal scientific and philosophical framework for understanding identity as a dynamical process rather than an ontological substance. Moving beyond traditional psychological or metaphysical views that treat identity as a fixed "self," the author proposes the Processual Identity Law. This law states that in any complex inferential system, "identity drift"—the continuous transformation of the self—is the generic, default state, while stability is merely a derivative effect of temporary constraints and attractors. Drawing on Dynamical Systems Theory, Information Theory, and Lacanian Psychoanalysis, the paper models identity as an inference derived from finite observation windows. It provides a structural explanation for phenomena often labeled as "identity crises" or "losing oneself," reframing them not as pathologies or failures, but as lawful transitions between dynamical regimes. Key Contributions: Mathematical Formalization: Defines identity as a time-indexed description of system trajectories. Structural Constraint: Proves that drift is structurally necessary in systems lacking invariant variables. Interdisciplinary Synthesis: Bridges the gap between process philosophy (becoming) and the hard sciences of complex systems. Applicability: Offers new perspectives for cognitive science, AI agent modeling, systems biology, and organizational theory.