Few-Percent Coherence Spread in Leakage-Driven Overlap Networks: A Toy-Model Note for Persistent Uncertainty and No-Absorbing-State Dynamics

This note investigates whether a few-percent coherence spread can arise naturally in leakage-driven overlap networks within the persistent uncertainty and no-absorbing-state framework. The starting point is the constraint that global uncertainty cannot be fully encoded within any finite, horizon-bounded domain. This implies boundary-mediated openness and persistent perturbations in local coherence dynamics. A minimal two-dimensional overlap network is introduced as a toy model. Each node evolves under local coherence production, dissipation, spatial smoothing, and irreducible leakage. A parameter sweep shows that a fractional coherence spread in the range of a few percent is not universal, but appears robustly within a regime of modest leakage and weak-to-moderate smoothing. The result is not presented as a cosmological prediction. Its significance is structural: threshold-governed coherence systems can naturally exhibit percent-level spreads, and such spreads can control transitions between subcritical, metastable, and reconfiguring regimes. This work serves as a quantitative companion to the no-absorbing-state framework, illustrating how persistent uncertainty can produce controlled deviations from exact stationarity while preserving long-lived coherent structure. Full mathematical formulation and numerical illustration are provided in the attached PDF.