Invariant Temporal Ordering Framework (ITOF) V15: Physical Realization and Residual Reassignment Under Invariant Ordered Succession

This preprint presents Version 15 of the Invariant Temporal Ordering Framework (ITOF), a foundational framework defining time as invariant ordered succession rather than measurable duration, accumulated change, dynamical flow, physical substance, or deformable temporal entity. Temporal ontology is represented as T_ITOF = (S, <), where S denotes physically admissible states and < denotes invariant ordered succession. The central contribution of V15 is a physical-realization and residual-reassignment architecture. Physical influences possess influence-character, represented as E_i = E_i(Pi_i), while time does not. In this formulation, time does not carry the constitutive properties by which physical influences act. Measured evolution is therefore assigned to physical realization under invariant ordered succession, through the relation Delta X_A under T_ITOF = F_A(Theta_A, E_A), where Theta_A denotes the system’s response-structure and E_A denotes the realized aggregated influence profile. V15 assigns residual differences between systems to physical realization rather than temporal deformation. The residual delta_A|B under T_ITOF is assigned to differences in Theta_A, Theta_B, E_A, and E_B, with the central closure that a nonzero residual does not imply deformation or variation of T_ITOF. The framework preserves measured relativistic asymmetries as operational physical data while rejecting the necessity of interpreting them as deformation of time itself. It develops experimental architecture, influence-profile and response-structure classification, coefficient grounding, operational geometry, limitations, challenge conditions, and a transition from V14 to the present V15 formulation.