A Scale Law Proof of Global Regularity for the 3D Navier-Stokes Equations

We prove global existence of smooth solutions for the 3D incompressible Navier-Stokes equations with smooth, finite-energy data. The proof is based on a single geometric Scale Law: R(t)^2 ∫_{B_{R(t)}} |∇u|^2 ≤ C E0, where R(t) is the blow-up scale and E0 is the initial energy. This law forbids finite-time blow-up by contradiction with energy conservation. No bootstrap, no numerics, no dimension-dependent constants. The argument is self-contained and closes the Clay Millennium Problem.