Operator Stability and Classical Emergence: A Regime-Based Criterion for Observable Invariance (IM-E002, v0.3)

This document is part of the Informational Mechanics (IM) framework and is published in the IM-E (Measurement & Operators) series within the IM v0.3 corpus. The paper formalizes an Operator Stability Condition (OSC) that specifies when quantum-mechanical observables exhibit regime-stable invariance under admissible disturbance. Rather than introducing new dynamics or modifying quantum theory, the analysis provides a structural criterion for when operator-defined quantities become persistently comparable and support classical description. Classical emergence is treated as a consequence of operator stability: when observables retain invariant content under admissible measurement and environmental interaction, effective classical structure arises without invoking collapse models, hidden variables, or additional ontological assumptions. The paper introduces no new axioms, dynamical mechanisms, or empirical fits. Its purpose is operational and disciplinary: to clarify the admissibility conditions under which classical description remains scientifically meaningful and to connect foundational admissibility constraints (IM-C series) with downstream structural consequences (IM-D series).