TOPOLOGY OF EMERGENCE: BETTI NUMBERS, BINOMIAL BENCHMARK, AND THE PRINCIPLE OF TOPOLOGICAL PRESENCE IN SISTEM MANAGEMENT

This paper develops a Topological frameworked for Emergence in networked systems, using simplicial complexes, Betti numbers, and Wasserstein-1 distance to binomial benchmark to quantify structural helth. It formulates the Law of Topological Self-Suppression of Control and derives the Principle of Topological Presence-validated on Arctic reclamation data via NDVI trends-to guide management through targeted, small-scale interventions that close critical cycles.