Local Admissibility Does Not Imply Identity Preservation - A Clarification of a Hidden Inference in Continuously Updating Systems

This project provides a formal clarification of a previously implicit inference underlying adaptive and continuously updating systems: that local admissibility of change is assumed to guarantee preservation of system identity over time. While this assumption is widely relied upon in practice, it is not generally valid. The registration makes this inference explicit and formally negates it using a Δ-based coherence and definability framework. It clarifies that a system may remain locally admissible at every update step while nevertheless crossing an unmarked threshold in which identity becomes undefined. In this condition, failure manifests not as error or instability, but as loss of definability despite continued local correctness. This work does not introduce a new theory, boundary, metric, or implementation. It serves to stabilize interpretation of prior Identity Preservation Boundary work by naming the false inference that boundary corrects, situating identity preservation as a transport- and implementation-independent constraint operating across time rather than at individual updates. The project is conceptual and clarificatory in nature. Its purpose is to define scope, prevent misattribution, and establish public precedence for the explicit negation of this hidden assumption in continuously updating intelligent systems.