Invariant Temporal Ordering Framework (ITOF) V17: Implementation-Conditioned Domain-Realization Law under Invariant Ordered Succession

This record presents Version 17 of the Invariant Temporal Ordering Framework (ITOF), titled: Invariant Temporal Ordering Framework V17: Implementation-Conditioned Domain-Realization Law under Invariant Ordered Succession. V17 develops ITOF into a mature implementation-conditioned, class-conditioned domain-realization formulation under invariant ordered succession. It preserves the temporal ontology established in V15, where time is defined as invariant ordered succession: TITOF = (S, ≺) and where temporal ordering is separated from measurable physical difference: Sᵢ ≺ Sⱼ ≠ ΔXᵢj V16 developed predictive physical-realization closure by treating calculated and observed residuals as tests of physical-realization adequacy rather than as direct evidence of temporal deformation. V17 extends this architecture by formulating measurable realization inside bounded physical domains, specified systems or response classes, realized influence profiles, surrounding environments, and operational measurement structures. The central V17 law is: ΔXAD |ₓ₈ₓ₎₅ = FAD (ΘA, ℰAD, CA) Here ΘA denotes the response organization of system A, ℰAD denotes the realized domain-specific influence profile, and CA denotes the surrounding physical environment or local physical context in which realization occurs. V17 further strengthens the implemented-domain structure by making domain realization class-conditioned: (D, A ∈ Θₖ, ΘA, ℰAD, CA, Gₘeas) ⇒ ΔXA^D, obs This means that an implemented domain is not an unrestricted claim over all systems in abstraction. It is a bounded physical-realization test applied to a specified system or response class within a specified domain. V17 also develops response classes Θₖ, high-level living and nonliving response-organization classes, member-level variation, exceptional conditions QA, outcome modes OAD, controllability, predictive comparison, model error, operational measurement structures Gₘeas, and relativistic-type reassignment. The central residual closure remains: δA|BD ≠ 0 ⇏ δTITOF ≠ 0 Measured asymmetry is preserved as real physical data, but its ontological assignment is fixed at the level of physical realization and operational measurement, not deformation of invariant temporal ordering. V17 does not claim complete numerical derivation of all physical domains. It establishes a structural and ontological assignment for domain realization: measured outcomes, residuals, environmental effects, system-class differences, and measurement asymmetries are assigned to physical realization under invariant ordered succession, not to deformable time.