A Measurable Geometric Depletion Program at the Dissipation Scale for 3D Navier-Stokes

This version expands the analytical framework of the previous F/C ratio protocol. It introduces a formal program toward conditional regularity for the 3D incompressible Navier-Stokes equations by defining a measurable geometric signature at the dissipation scale (t). The draft integrates 1D sparseness hypotheses with majority-direction coherence parameters to define an effective sparseness ₄₅₅ (t) and a depletion margin (t). It connects these observables to a local-BMO endpoint continuation route and provides an implementable diagnostic algorithm for DNS validation. This is an expanded and more analytical version of the initial framework (formerly DOI: 10. 5281/zenodo. 18263794). It shifts the focus from a global ratio to a localized geometric depletion program at the dissipation scale.