ψ-Lagrangian Universe: A Minimal Retentional Framework for Late-Time Cosmology

This work introduces a minimal Lagrangian formalism for retentional behaviour in the late Universe. Motivated by empirical signatures—persistent suppression of the growth index, a scale-invariant k-plateau, and the sharp structural transition near z† ≈ 1.7—the ψ-framework replaces dynamical evolution with structural persistence. The model is built from three core elements: the structural differential Δψ, the retentional node Ξ, and the pseudotime parameter τ. A compact ψ-Lagrangian is formulated, and its Euler–Lagrange equations describe the evolution of difference as retention rather than motion. The article presents this architecture with academic restraint, as a formal mathematical model of a specific empirical regime, without making claims of universality. Figures illustrate the k-plateau, the structural potential, and the bifurcation at the characteristic redshift z†.