What question did this study set out to answer?

The aim is to develop a structural formulation for the late-time dark-energy regime within the CoreLumen framework.

February 25, 2026Open Access

CoreLumen III: Transition from Dark-Matter Scaling (R2) to Lyapunov Dark-Energy Regime (R3) — Zenodo Archival Structural Edition v2.0

Key Points

The aim is to develop a structural formulation for the late-time dark-energy regime within the CoreLumen framework.
Construct an autonomous dynamical system for exponential potentials.
Derive conditions for convergence toward a scalar-dominated Lyapunov attractor.
Analyze the effects of parameters λ and γ on the R2→R3 transition.
Establish stability and acceleration conditions for the Lyapunov attractor.
Identify a continuous ΛCDM limit while maintaining tensor propagation.
Demonstrate a minimal leakage parameter affecting the duration of R2 scaling.

Abstract

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.

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