CoreLumen Cosmology IX : Late-Time Dynamical Closure

This work analyzes the late-time dynamical structure of the CoreLumencosmological framework. Within the CoreLumen program the physical vacuum is interpreted as acondensate medium described by the complex order parameter Ψ = ρ e^{iθ}. In this picture the phase dynamics of the condensate organizes thegravitational response of the vacuum sector and can influence thelarge-scale evolution of the universe. The present work formulates the dynamical system describing thephase flow of the condensate vacuum and investigates the emergenceof a stable late-time attractor associated with cosmic acceleration. Using a dynamical systems description of the cosmological evolution,the framework identifies fixed points of the phase flow and illustrateshow the cosmological system evolves toward a stable accelerated regime. This attractor interpretation provides a dynamical explanation oflate-time cosmic acceleration without introducing a finely tunedcosmological constant. This document is released as a Zenodo archival version whose purposeis to establish the conceptual structure of the attractor dynamicswithin the CoreLumen cosmology program and to define the frameworkfor future numerical implementations of the model.