Deriving the Coherence Threshold _From Stochastic Boundary Dynamics to Self-Referential Interiority in a Minimal Computational Model_

Complex systems continuously experience environmental perturbation, yet many maintain stable internal organization across time. This paper examines a simple principle that may govern this transition. A system enters a persistent interior regime when the rate at which it restores internal organization exceeds the rate at which environmental interactions disrupt that organization. When this condition is sustained, system states increasingly reflect the influence of prior internal dynamics rather than immediate external perturbation. To explore this idea, a minimal computational model is constructed using the period lattice, a discrete two-dimensional structure in which four binary poles meet at each junction to form five possible cluster configurations. Local probabilistic restoration rules interact with stochastic environmental disruption to produce a simple dynamical field. The balance between these processes is characterized by the ratio R = λ_self / λ_env representing internal restoration relative to environmental disruption. Simulations show two distinct behavioral regimes. When disruption dominates, perturbations remain local and the lattice exhibits noise-like dynamics. When restoration dominates, corrective interactions propagate through overlapping clusters and generate extended domains of correlated structure. The model therefore illustrates how a threshold in the balance between restoration and disruption can give rise to sustained self-stabilizing organization. Although highly simplified, the lattice provides a reproducible computational demonstration of the coherence threshold principle and offers a concrete dynamical interpretation of the Law of the Interior within the broader Aleph Harmonic Qualia framework.