This archival volume develops the structural formulation of the late-time dark-energy regime (R3) within the CoreLumen phase–condensate framework. Starting from the breakdown of matter-like scaling in Regime R2, we derive sufficient conditions for convergence toward a scalar-dominated Lyapunov attractor under effective-field-theory validity and kinetic positivity. An autonomous dynamical system is constructed for exponential potentials, yielding explicit existence, stability, and acceleration conditions classified by the parameter λ. A minimal leakage parameter γ governs the finite duration of the R2 scaling epoch and determines the temporal structure of the R2→R3 transition. The framework admits a continuous ΛCDM limit (γ → 0, λ → 0) while preserving tensor propagation (cT = 1) and avoiding phantom instabilities. This volume serves as a self-contained structural reference for the dark-energy sector of CoreLumen Cosmology.
Jaegue Hwang (Mon,) studied this question.