TEBAC Navier--Stokes Program I: Spectral Stokes Foundation and Critical Cascade Ledger

This preprint is the first entry module of a TEBAC-based modular program toward the three-dimensional incompressible Navier--Stokes existence and smoothness problem. The manuscript works on the periodic domain \(\mathbb T^3\) and develops a rigorous foundational layer for the program: the Leray projection, the divergence-free Hilbert space, the Stokes operator \(A=-\mathbb P\Delta\), the Galerkin approximation scheme, the classical \(L^2\)-energy identity, the vorticity/vortex-stretching ledger, dyadic spectral packets, triadic Fourier interactions, and the first TEBAC cascade-defect formalism. The main purpose of the paper is not to claim a complete solution of the Navier--Stokes Millennium problem. Instead,…