A Causal-Geometric Framework for Navier-Stokes Regularity

This work develops a causal–geometric formulation of fluid dynamics in which the classical incompressible Navier–Stokes equations arise as emergent projections of an underlying cymalogical structure. Within this framework, discrete causal impulses (khrons) originating in the external space "Z_0" generate a metageometric smoothing kernel that naturally regulates high-frequency behaviour. The resulting causal contribution suppresses the mechanisms responsible for potential finite-time singularity formation in the classical formulation while preserving large-scale fluid behaviour. The analysis shows how the khron-induced regularization provides strengthened conceptual control over gradient growth, energy transfer, and dissipation. A modified Kolmogorov spectrum and reduced intermittency emerge in the turbulence regime, reflecting geometric constraints inherited from the underlying causal structure. The approach remains fully compatible with classical phenomenology in the limit β → 0, while simultaneously clarifying the origins of small-scale stability. The present results are consistent with the broader cymalogical program and its independent cross-domain coherences, including the JWST structure-emergence threshold, high-precision hydrogen fine-structure spectroscopy, and the 20 GeV20 Fermi–LAT excess in the Milky Way halo. ------- Keywords: Cymalogical Fluid Dynamics • Navier–Stokes Regularity • Causal Geometry • Metageometric Kernel • Turbulence • Kolmogorov Spectrum • Energy Cascade • High-Frequency Suppression • Structural Regularization • Mathematical Physics • Incompressible Flow • Hydrodynamics • Nonlinear PDE • Emergent Dynamics • External Causal Space • Khron Mechanics • Open Science.