Invariance of BKM and Prodi-Serrin Integrals under Bounded Temporal Lifting

The incompressible Navier-Stokes equations on T³ exhibit a structural asymmetry: the spatial domain inherits the compact geometry of R³/Z³, while the temporal axis remains unbounded and analytically unconstrained. Classical approaches treat time as a neutral parameter, a clock labeling solution states without participating in the analytic structure. On periodic domains, this separation forfeits geometric constraints that the lattice structure naturally provides. We construct a coupled system (U, φ) via a bounded vorticity-response functional and prove that the Beale-Kato-Majda and Prodi-Serrin regularity criteria are invariant under this bounded temporal lifting. Numerical validation on grids up to 256³ confirms invariance to machine precision across Reynolds numbers spanning 10³ to 10⁸.