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: (d^2 Xi / dt^2) + R(psi)(dXi/dt) + Lambda_psi Xi = 0 In the stationary regime, this reduces to: dXi/dt = - kappa Xi where kappa = Lambda_psi / R(psi) is a control parameter with dimension T^-1. The system admits an exponential relaxation solution: Xi(t) = Xi_0 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.