Global Regularity of the 3d Navier-Stokes Equations: The Nonsingular Finality via Intrinsic Topological Back-Reaction (Stage 3)

In this final installment (Stage 3), we establish the absolute global regularity and weak-strong uniqueness of the 3D incompressible Navier-Stokes equations. We bridge the purely analytical time-independent H m bounds established in Stage 2 with a profound geometric framework: the Intrinsic Topological Back-Reaction. By lifting the fluid domain to a 4D manifold, we demon- strate that the finite-time blow-up dictated by the Beale-Kato-Majda (BKM) criterion is not only analytically suppressed but topologically obstructed. The viscous dissipation mimics the Ricci flow, driving the system toward a globally smooth, singularity-free generalized manifold.