Topological Persistence of the Vacuum: A Retentive Framework for Late-Time Cosmology and Structural Invariants

This paper develops a formal framework in which topological persistence serves as the primary descriptor of late-time cosmic structure. It introduces the Retentive Floor (Δψ₀), Ξ-nodes, and the equilibrium term Λψ as structural invariants that remain finite when classical dynamical evolution weakens. The theory explains correlation-time plateaus, void residuals, and suppressed potential evolution through a retentive rather than dynamical mechanism. The approach unifies cosmological, topological, and structural-physical regimes into a coherent model of metric-independent continuity.