Invariant Temporal Ordering Framework (ITOF) V20: Ontological Assignment Closure under Invariant Ordered Succession

This record contains Version 20 of the Invariant Temporal Ordering Framework (ITOF), titled *Ontological Assignment Closure under Invariant Ordered Succession*. V20 formulates the general non-transfer principle for measurement, clock systems, operational success, model correction, system outcome, and relativistic interpretation. The fixed ITOF temporal ontology remains: T_ITOF = (S, ≺) where S denotes distinguishable states and ≺ denotes invariant prior–subsequent ordering. Time is therefore treated as invariant ordered succession, not as matter, energy, force, field, clock output, measurement geometry, or causal influence. The manuscript distinguishes ordered succession from measured physical change: S_i ≺ S_j ≠ ΔX_ij and assigns measured realization to system structure, realized influence profile, and local environmental configuration: ΔX_A^D | T_ITOF = F_A^D(Θ_A, E_A^D, C_A) Here Θ_A denotes the response organization of system A, E_A^D denotes the realized domain-specific influence profile, and C_A denotes the local environmental configuration. This relation states that measurable change occurs under invariant ordered succession, while physical production remains assigned to systems, influences, and environments. V20 also formalizes the measurement non-transfer principle: P_NT: Q_meas/model/system ⇏ δT_ITOF ≠ 0 where Q_meas/model/system denotes measured outputs, clock differences, model corrections, operational successes, system outcomes, or formal measurement relations. The principle states that measurement and modeling success do not by themselves establish deformation or alteration of invariant temporal ordering. Clock systems are treated as human-organized symbolic measuring systems: G_meas(A_clock) = N(P_reg) ≠ T_ITOF A clock converts a selected regular physical process P_reg into a numerical symbolic reference N(P_reg). Clock drift, divergence, correction, or failure remains assigned to the physical realization of the clock system, not to temporal ontology: Δτ_clock ≠ 0 ⇏ δT_ITOF ≠ 0 Relativistic measurement is accepted as operationally successful where it succeeds. V20 rejects only the further ontological transfer from successful relativistic measurement to physical deformation of invariant temporal ordering: Δτ_A ≠ Δτ_B ⇏ δT_ITOF ≠ 0 The manuscript also distinguishes geometric representation from temporal ontology: G_geom ≠ T_ITOF and more generally: Success(G_meas, M_model) ⇏ OntologicalTransfer(T_ITOF) Building on V15–V19, V20 consolidates temporal ontology, residual reassignment, predictive closure, implementation-conditioned realization, outcome assignment, and relativistic reassignment into a general assignment-closure framework. Its central claim is that measurement systems, models, clocks, formal geometries, and operational successes may organize the representation of ordered change, but they do not define the ontology of time.