Stabilisation Dynamics III: Propagation in Stabilisation Lattice Dynamics (Finite-Range Correlations Without Criticality)

This paper investigates spatial propagation in stabilisation lattice systems with local coupling and weak noise. Building on the geometric stabilisation framework, it shows that correlations propagate over a finite length scale determined by the balance between coupling strength and local stabilisation curvature. The results demonstrate that stabilisation systems exhibit exponential decay of correlations and do not display conventional critical behaviour, instead forming a class of screened propagation systems. This work forms part of the “Stabilisation Dynamics” series, which develops a geometric framework for probability, correlation and dynamical behaviour in stabilisation systems. Subsequent work extends this framework to continuum limits, domain growth and operator-based resolution structure.