Geometric Vorticity Control ver.3 with Supplementary Material ver.2

This paper presents a constructive geometric framework for generating classical solutions to the three-dimensional incompressible Navier–Stokes equations. The proposed method extends the Coherence Tube Density (CTD) framework to a spherical formulation by introducing a three-dimensional radial coherence structure. Representative vectors are extracted from concentric spherical layers, from which representative particle trajectories are constructed. The collection of these trajectories is then synthesized into a particle ensemble that reconstructs the velocity, pressure, and vorticity fields. The framework combines spherical coherence analysis, layered (Baum-Kuchen) decomposition, trajectory synthesis, and kernel-based field reconstruction into a unified geometric approach. It provides a constructive interpretation of fluid motion and investigates the resulting regularity through coherence-based spacing constraints. This repository contains the manuscript describing the proposed framework.