Invariant Temporal Ordering and System-Dependent Physical Evolution: A Structural Framework with Empirical Discrimination Criteria

This work presents the Invariant Temporal Ordering Framework (ITOF), a structural formulation in which time is defined as an invariant relational ordering of physical states rather than a dynamical or causal entity. The framework establishes a clear distinction between temporal ordering and physical evolution. Temporal ordering provides the invariant structure of succession, while observable variation arises from system-dependent physical processes governed by internal structure, interactions, constraints, and environmental conditions. A generalized structural descriptor, Ψ(S), is introduced to represent how physical systems realize change under multi-factor influences. This formulation preserves compatibility with established physical theories, including relativistic descriptions, while providing a distinct explanatory structure. In this version (V9), the framework advances beyond conceptual interpretation by introducing a formal empirical discrimination criterion. Observable rates are compared across distinct physical systems under identical external conditions, and residual variation is defined as a measurable deviation from unity in their ratio after accounting for known effects. The framework predicts that: If all systems exhibit identical proportional variation within experimental uncertainty, interpretations based on universal temporal variation are supported.If reproducible residual deviations are observed across independent systems and measurement channels, the variation is attributed to system-dependent physical evolution. This establishes the framework as an empirically discriminable structural interpretation of time, in which its validity depends on measurable outcomes rather than conceptual assumptions alone.