A Unified Mathematical Framework for Persistence Beyond Dynamics (ψ-RFT)

This work develops ψ-Retentive Field Theory (ψ-RFT) — a unified mathematical framework describing how physical, biological, and informational systems retain measurable difference (Δψ) under temporal collapse, metric degradation, or observational absence. The theory introduces the retentive node Ξ, defines a ψ-metric G_{\psi}^{\mu\nu}, derives the ψ-Lagrangian on pseudo-time τ, and establishes four structural theorems (P, G, T, S) governing nucleation, geometric stability, temporal persistence, and structural invariance. Applications include retention cosmology, ψ-neutrino coherence, pre-biological structural formation, and non-violative ψ-AI. The framework formalizes a class of regimes in which structure persists even when classical dynamics vanish.