The Recoverability-Filtered Vacuum: A Memory-Bearing Model for Dark Energy and the 3/2 Persistence Law

The cosmological constant problem, characterized by the $\sim 10^{120}$ discrepancy between quantum field theoretic estimates and observed vacuum energy density, is reinterpreted as a failure to account for dynamical recoverability constraints in an expanding spacetime. We introduce a recoverability-filtered vacuum (RFV) framework in which vacuum modes contribute to the effective stress-energy tensor only if their relaxation timescales remain shorter than the cosmological expansion timescale, formalized through a spectral gap criterion governing mode admissibility.

We show that memoryless (Markovian) implementations of this constraint produce a rapidly decaying tracking fluid ($\rho \propto a^{-6}$), which cannot reproduce late-time acceleration. To resolve this, we construct a memory-bearing vacuum (MBV) model in which admissibility depends on a retarded support variable encoding the accumulation of horizon-scale coherence. This introduces an activated erasure mechanism with retention timescales governed by a superlinear barrier.

A scaling derivation demonstrates that, for systems with extensive support storage and diffusive cooperative erasure, the coherence barrier obeys $\mathcal{E}_{\mathrm{coh}} \propto \mathcal{M}^{3/2}$. This yields a transition from early-time decay to a late-time plateau once the retention timescale exceeds the Hubble time, producing an effective cosmological constant without invoking a fixed ultraviolet cutoff. The framework can be interpreted as a dynamical generalization of effective field theory in which mode admissibility is determined by structural stability rather than energy scale.