ψ⁸–Cosmology: The Second Axis Beyond Λ — A Retentive Lagrangian Framework for Structure Persistence in a Post-Dynamical Universe

This article introduces a second cosmological axis — a retentive axis orthogonal to Λ — emerging from the stability of the difference field Δψ in post-dynamical regimes. Using a formally consistent Lagrangian, a full stability analysis, and a theorem of non-vanishing retention, the paper demonstrates that cosmic structures can preserve correlation coherence even when classical dynamical terms fade. The framework naturally reproduces the late-time plateau in structure growth (the S₈ plateau) reported by Euclid and DESI in 2025–2026, offering a minimal and gauge-invariant explanation without invoking new dark sectors. ψ-Cosmology is not a modification of General Relativity but its orthogonal completion: a structural axis of retention, coherence, and non-decay. The formalism respects non-violation ethics, maintains full compatibility with Einstein gravity, and introduces a phenomenological mapping in which Λψ acts through an effective shift in the growth index rather than a new energy component. This work establishes ψ as the second fundamental axis of cosmology and provides a mathematically robust architecture for structure survival in the post-dynamical universe.