Λψ: Retentive Invariants Beyond Dynamical Cosmology

This work introduces a post-dynamical interpretative framework for late-time cosmology based on the concept of retention—the capacity of large-scale cosmic structures to preserve form and correlation beyond the phase of active dynamical growth.

Motivated by persistent observational tensions, most notably the reduced clustering amplitude quantified by the parameter S_8, the paper proposes a minimal phenomenological invariant, \Lambda_\psi, describing structural persistence rather than dynamical acceleration. The framework does not modify gravity, introduce new particle species, or alter the standard dynamical equations of \LambdaCDM. Instead, it operates as a complementary interpretive layer applicable once large-scale structure formation has effectively saturated.

The retentive invariant is formulated to characterize a late-time regime in which cosmic filaments, voids, and correlation patterns exhibit long-term stability despite continued expansion. This regime is identified through model-independent observational criteria, including scale-stable correlations and plateau behavior in clustering amplitudes.

A methodological protocol based on the principle of non-violation is introduced to ensure minimal theoretical intrusion in data interpretation. The work emphasizes falsifiability, clearly defined domains of applicability, and explicit interpretive limits.

The proposed framework offers a coherent, non-invasive explanation for late-time cosmological anomalies and reframes large-scale structure as a memory-bearing architecture rather than an endlessly evolving dynamical system.