Interface Event Dynamics: A Navier–Stokes Regularity Framework Based on the Universal Tear Axiom

This work proposes the Universal Tear Axiom (UIE) for 3D incompressible Navier–Stokes flows: all potentially singular dynamics concentrate in a countable set of localized space–time neighborhoods we call Tempore Ruptis (“breaks in time”), where viscosity dominates. Assuming UIE, we establish a conditional global regularity and uniqueness result for finite-energy Leray–Hopf solutions. The proof reduces the millennium-level difficulty to two testable ingredients: (1) a finite-overlap decomposition of space–time into a quiescent background plus Tempore Ruptis; and (2) a universal, non-singular similarity profile inside each neighborhood that enforces standard LPS/BKM bounds locally—and thus globally via summation over the cover. We outline falsifiable predictions for DNS/experiments (localization, rescaled profile universality, bounded local norms) and sketch event-aware turbulence closures that activate dissipation only within detected Tempore Ruptis. The framework offers a physically grounded and mathematically tractable pathway from local viscous regularization to global smoothness. Keywords: Navier–Stokes; global regularity; Tempore Ruptis; viscosity-dominated similarity; LPS/BKM criteria; turbulence modeling; Leray–Hopf solutions