Attainment of a Scale-Critical Vortex-Stretching Functional in Three Dimensions

We prove that a scale-critical quartic vortex-stretching functional on divergence-free H^1 vorticities over R^3 has a finite positive supremum and that the supremum is attained. The proof uses Calderon-Zygmund bounds, an explicit positive periodic seed localized by slow modulation, an exact two-parameter normalization, and concentration-compactness with Bogovskii divergence correction and off-diagonal pressure estimates. This is a static variational result and does not imply Navier-Stokes regularity.