Topology-Dependent Flux Lattice Persistence in Noisy Superconducting Films: A Modified Decay Law and Falsifiable Prediction

This is the fifth paper in the Relational Field Theory series. It extends the same minimal recurrence mechanism (already validated in quantum circuits, oscillator networks, neural networks, and reaction–diffusion systems) to superconducting films under thermal noise. Superconducting films under thermal noise are expected to exhibit exponential decay of vortex lattice order and transition to a melted state beyond a depinning threshold. Experiments with engineered pinning arrays motivate asking whether topology alone can shift apparent persistence thresholds. We propose a minimal phenomenological recurrence for local vortex coherence on the pinning lattice that reproduces standard exponential decay in uniform pinning but predicts delayed melting and nonzero order plateaus when repeated local motifs are present in the pinning grid. The model is parameterized by a single topology-dependent memory strength \alpha(\mu)and yields closed-form expressions for the order parameter r(d)with a calculable plateau height and build-up time scale. Matched-pair simulations or experiments (identical film size, temperature, applied field, differing only in motif density) provide a direct falsification protocol. If no separation is observed, the model is ruled out; if plateaus emerge as predicted, it offers a new diagnostic for topology-induced memory in noisy vortex dynamics.