Invariant Temporal Ordering and System-Dependent Physical Evolution: A Structural Framework for Time, Measurement, and Physical Description

This work presents Version V7.1 of the Invariant Temporal Ordering Framework (ITOF), a structural reinterpretation of time in which temporal ordering is understood as an invariant relational ordering of physical states rather than as a dynamical variable or independently measurable entity. Within this framework, temporal ordering provides the structural condition for the succession of states, while observable rate variation is attributed to system-dependent physical evolution, including internal structure, interactions, and external conditions. The formulation preserves consistency with established empirical observations, including relativistic effects, while introducing a distinct interpretive framework. Version V7.1 refines the conceptual presentation of the framework through a revised abstract, strengthened introduction, and improved conclusion, providing clearer articulation of the central distinction between invariant temporal ordering and system-dependent physical behavior. An executive summary is included to enhance clarity and accessibility. The mathematical structure remains unchanged, expressing observed rates relative to invariant temporal ordering while incorporating system-dependent contributions through a phenomenological term Ψ(S), interpreted as an effective structural descriptor rather than a fundamental parameter. The framework does not modify established physical laws or empirical predictions. Instead, it provides a structured reinterpretation of temporal measurement and rate variation by attributing observable differences to physical systems rather than to variation in time itself. This version is intended as a refined and stabilized presentation of the V7 framework, improving clarity, consistency, and interpretive precision without introducing new theoretical components.