Λψ-Retention II: A Minimal Dynamical System for Stationary Growth and Structural Saturation

We present a minimal dynamical system describing the emergence of a stationary growth regime in late-time cosmology. Extending the Λψ-retention framework, we show that a balance between retentional resistance and structural stabilization leads to a controlled suppression of growth. We formulate a phenomenological second-order equation governing structural evolution: (d² Xi / dt²) + R (psi) (dXi/dt) + Lambdaₚsi Xi = 0 In the stationary regime, this reduces to: dXi/dt = - kappa Xi where kappa = Lambdaₚsi / R (psi) is a control parameter with dimension T^-1. The system admits an exponential relaxation solution: Xi (t) = Xi₀ exp (-kappa t) which describes convergence toward a stationary state. Within this regime, the growth index γ can be interpreted as an effective phenomenological parameter governed by the ratio kappa. This provides a minimal quantitative basis for interpreting the observed growth plateau (γ ≈ 0. 64) as an emergent property of retentive dynamics. The model supports a transition from a growth-dominated cosmological regime to a regime of structural stabilization.