Stabilisation Dynamics VI: Domain Growth in Stabilisation Lattice Dynamics (Sub-Curvature Coarsening from Finite-Range Propagation)

This paper investigates the dynamical formation and growth of domains in stabilisation lattice dynamics. Starting from disordered initial conditions, we measure the evolution of characteristic domain size using sign-field correlations. We find that domain growth follows an approximate power law L(t) ~ t^alpha with exponent alpha ≈ 0.39, which is smaller than the value expected for curvature-driven coarsening in standard ordering systems. This slower growth indicates that domain evolution is governed by finite-range stabilisation propagation rather than curvature-driven dynamics. Within the geometric stabilisation framework, ordering spreads through local basin interactions, leading to gradual, locally mediated coarsening consistent with a screened propagation mechanism. Together with previous results on probability, correlation, spatial propagation and the absence of criticality, these findings provide a unified geometric description of both static and dynamical structure formation in stabilisation systems. Subsequent work further extends this framework through operator-based resolution dynamics and phase structure.