ψ⁸: A Simulation Framework for Retentive Difference, Node Persistence, and Structural Stability

This paper introduces the ψ⁸ Retentive Simulation Framework (ψ-SIM), a unified method for measuring the retentive difference Δψ, persistent node density Ξ, and the stabilizing parameter Λψ across cosmological, acoustic, and materials-science domains. The framework formalizes ψ-pseudo-time τψ, develops the retentive Lagrangian, and provides a transparent simulation protocol capable of identifying retentive plateaus and node-stability basins. Through cross-domain reproducibility — including consistency with Euclid weak-lensing plateaus, LSST morphology stability, acoustic retention curves, and materials-science variance minima — ψ-SIM demonstrates that structural persistence is a measurable and scalable physical principle. The model is designed for integration into scientific pipelines and long-term archival as part of the evolving retention-based physics ecosystem.