The Master Equation of Spectral Hydrodynamics: Variations, Regimes, and Projections on Noetic Planes Patrice PORTEMANN December 2025 Abstract This technical document explicates the general form of the equation governing the Koïlon substrate and details its variations as a function of the Noetic Reynolds Number (ReN). We subsequently present the "Dominance Matrix," identifying which term of the equation governs the dynamics for each Noetic Plane (E1 −E7). This formulary serves as a unified mathematical reference for the set of preceding volumes. 1 Canonical Form and Terms The evolution of the vacuum velocity field v is governed by the noetic extension of the Navier- Stokes equation. This form unifies classical fluid mechanics and the topological constraints of the quantum vacuum: ρk Dv Dt | {z } Inertia (Mass) = −∇Pζ | {z } Pressure + v × T | {z } Tension (Energy) + η(Sent)∆v | {z } Viscosity (Information) (1) Definition of Variables: • ρk: Constant density of Koïlon (1.4 × 1010 ANU/fundamental volume unit). • Pζ: Entropic vacuum pressure, proportional to ζ(−1)e−Suniv. It is the engine of expansion and gravity. • T : Torsion Field (Spin-Density). […]