Global Regularity of the 3D Incompressible Navier-Stokes Equations via Generative OS Geometry and the M/E/S Confinement Structure

This paper introduces a generative geometric framework, termed OS Geometry, to establish the global regularity of the 3D incompressible Navier-Stokes equations. By redefining the geometric singularity not as a point in space, but as a pre-geometric zero-information state (OS-atm) and a directional anisotropic state (OS-dir), we demonstrate that finite-time blow-up is structurally impossible. The proof synthesizes the position-scale-time (M/E/S) confinement structure, anisotropic dissipation via the OS-Laplacian, and scale-resolved generative equations (OSG2ADV). The theoretical results are robustly corroborated by the Katsumasa Engine, a highly parallelized computational solver demonstrating unconditional stability and monotonic vorticity decay under extreme conditions.