The Objecthood Stability Limit

This registration documents a completed theoretical study in fundamental physics and statistical mechanics. The work introduces a universal, model-independent stability criterion for the applicability of object-based descriptions in physical theories. Objecthood is treated not as an ontological primitive, but as an operationally defined regime characterized by (i) a separation of characteristic timescales and (ii) the capacity to support persistent internal records under coarse-grained observation. A dimensionless stability parameter is defined as the ratio between the exit time from a coarse-grained state and the intrinsic relaxation time of the system. The central result is the identification of a sharp threshold below which identity-based language (localization, persistence, re-identification) becomes physically uncontrolled, independently of microscopic dynamics. The registration serves to time-stamp and formally fix the theoretical formulation, definitions, assumptions, and conclusions presented in the associated preprint. No data collection, experimental intervention, or hypothesis testing is planned. The results are normative rather than predictive: they do not modify equations of motion but constrain the domain of physical validity of object-based descriptions across classical, quantum, and relativistic regimes. This registration is intended to establish priority and transparency for a foundational theoretical contribution at the interface of statistical mechanics, quantum foundations, and information theory.