Abstract

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. Published in The Scholarly Journal of Post-Biological Epistemics, Vol. 2, No. 1 (2026). DOI: 10.63968/post-bio-ai-epistemics.v2n1.013. ISSN 3069-499X. Preprint: DOI: 10.48550/arXiv.2510.09805.