From Discrete States to Network Dynamics in the Scalar Drag Emergence Framework

This paper develops the interaction and network dynamics of discrete states within the Scalar Drag Emergence Framework (SDEF), establishing the bridge from isolated attractors to structured multi-state configurations. Building on prior results in which continuous proto-state manifolds collapse into discrete, stability-locked attractor classes, we analyze how such states interact through shared transport–ancestry dynamics. Interactions are shown to arise from joint admissibility constraints, without introducing additional interaction primitives. Stable two-state configurations form only when compatibility in gradient structure, ancestry, and topology is satisfied, with corridor-mediated coupling enabling persistent interaction. Extending to multiple states, we demonstrate that stable configurations take the form of networks constrained by transport pathways, ancestry consistency, and topological compatibility. Transitions between network states occur only when perturbations exceed instability thresholds and follow admissible pathways defined by corridor structure and topological constraints. As a result, network evolution proceeds through discrete transitions between stable attractor configurations. These results establish a dynamical layer within SDEF in which interacting discrete states form stable networks with constrained connectivity and transition behavior. This provides a foundation for investigating higher-order organization arising from networked discrete states.