Retentive Bifurcation in a ψ–Ξ Pair: Stability Criterion and a Laboratory Analog Using a Noisy Optical Interferometer

This work introduces a minimal dynamical model for the onset of retentive behavior — the transition from exponential decay to persistent structure — using a coupled ψ–Ξ pair. A linear stability analysis identifies a single bifurcation parameter, μψ = bλ – aα, defining a retentive threshold: reinforcement dominates when bλ > aα. To demonstrate physical accessibility, the study proposes a table-top Mach–Zehnder interferometer with controlled feedback and injected noise. By tuning gain parameters, the experiment can reproduce correlation-time plateaus, noise-induced switching, and persistent imbalance — a laboratory signature of structural memory. The model is scale-independent and does not rely on cosmological assumptions. It provides a compact mathematical criterion, an experimental protocol, and a mechanical pathway for testing ψ-retention in controlled environments. Limitations are acknowledged for multivariate and nonlinear feedback, suggesting future extensions into multi-scale architectures.