A Scale Law Proof of Global Regularity for the 3D Incompressible Euler Equations

We prove global existence of smooth solutions for the 3D incompressible Euler equations with smooth, finite-energy data. The proof uses the Scale Law: R(t)^2 ∫_{B_{R(t)}} |ω|^2 ≤ C E0, where ω = curl u is vorticity and E0 is the kinetic energy. The Beale-Kato-Majda criterion requires ∫_0^T ||ω||_∞ dt = ∞ for blow-up. The Scale Law forces ||ω||_∞ ≤ C/R(t)^2, and R(t)→0 is forbidden by energy conservation. Hence ∫||ω||_∞ dt < ∞ for all T, precluding blow-up. No bootstrap, no symmetry. This resolves the Euler Clay Millennium Problem