Mathematical Structure of the Hyper-Luminal Propulsion Engine Flow Equations Coupled Within the Ktoe Framework

This paper presents the formal mathematical structure for the flow dynamics governing the Hyper-luminal Propulsion Engine, a deep-space transit mechanism integrated within the Khánh Theory of Everything (KToE). By mapping the internal engine fluid states to the reduced density matrices ρ24 and ρ8 derived from the 96-dimensional Khanhnions manifold, we eliminate the physical and mathematical singularities associated with conventional relativistic propulsion. The core mechanism relies on a dynamic topological phase shift that modulates the effective mass of the local field carrier, preventing mass divergence as velocities approach hyper-luminal thresholds across intergalactic geodesics toward the Andromeda galaxy.