EL Science Volume 5 (Revised): The Minimal 5-Variable Vacuum System Construction, Parameter Scan, and Robustness Verification of the Vacuum-Lifecycle Mechanism

EL Science Volume 5 (Revised) presents the first explicit vacuum-lifecycle mechanism inside the EL Science cyclic cosmology framework. Previous volumes established: a cyclic structural framework, a verified bounded nonlinear attractor, observational compatibility with Pantheon+ and DESI 2024 BAO data, and a dynamical imbalance bridge linking internal system evolution to cosmological dark-energy behavior. However, the physical mechanism responsible for closing the cosmological cycle remained unresolved. This revised volume introduces a minimal 5-variable extension of the verified EL Science dynamical system by adding a new vacuum-stability variable: V = vacuum stability where: V = 1 corresponds to a stable vacuum maintaining large-scale cosmic separation, V = 0 corresponds to a destabilized vacuum capable of activating cosmological transition and rebirth dynamics. The revised system introduces: one new dynamical equation, one new transition coupling term, and three phenomenological parameters: u (vacuum self-repair rate), m (compression-induced destabilization rate), η (vacuum-collapse transition activation strength). A complete 125-case parameter scan was performed using the verified Volume 3 Hopf-bifurcation regime as the base dynamical structure. The scan demonstrates that: 11 of 125 parameter combinations (8.8%) produce a fully healthy vacuum-flip cycle, all successful cases reproduce the predicted causal sequence:C_peak → V_min → Ψ_peak → R_peak, all successful trajectories remain bounded, and strong hysteresis/memory behavior emerges naturally from the vacuum dynamics. The cleanest verified case produces: V_min = 0.376, oscillation range = 0.614, period = 55.4 τ-units, and a large hysteresis loop area of 0.686. The framework now possesses an explicit tested causal mechanism in which: compression destabilizes the vacuum, vacuum destabilization activates transition, transition drives renewed expansion, expansion suppresses compression, and the vacuum gradually restores itself before the next cycle begins. This converts the vacuum-lifecycle concept from a verbal structural hypothesis into a mathematically verified dynamical mechanism. The volume explicitly documents limitations: the cycles remain repetitive rather than evolutionary, the mechanism is moderately robust rather than universal, and the parameters remain phenomenological rather than derived from first-principles quantum-vacuum physics. The next required test is pre-registered explicitly:testing whether the new 5-variable vacuum system preserves or improves the observational fit established in Volume 4 v2. Author: EL Boulos TaukYear: 2026