TEBAC Navier--Stokes Program III: Spectral Cascade Obstruction and Critical Resonance Absorption — Reduction Module

This preprint is the third module of the TEBAC Navier--Stokes program. It continues the spectral Stokes, Galerkin, vorticity-shell, and resonance-classification framework developed in NS-I and NS-II, and focuses on the large-data critical resonance absorption problem for the three-dimensional incompressible Navier--Stokes equations on the periodic domain \(\mathbb T^3\). The manuscript develops a theorem-bearing reduction framework for the critical high-frequency cascade. Starting from the coherent critical resonance residue isolated by the previous modules, it performs a sequence of spectral, helical, Beltrami, packing, axial, phase, and envelope reductions. At each stage, exact geometric cores are separated…