SMT-Vol.3 Seonggil Topology: Dynamic Phase Informatics and the Roa Axiomatic System

Classical topology is fundamentally constrained by the dogma of “Continuous Deformation.” This paper introduces Seonggil Topology, a revolutionary framework derived from Rough Operator Algebra (ROA). Building upon the foundations established in SMT-Vol.1 (DOI: 10.5281/zenodo.19755765) and SMT Vol.2 (DOI: 10.5281/zenodo.19758646), we discard the necessity of smooth connectivity, redefining topological spaces as discrete sets of logical states synchronized by the Alpha Resonance Golden Ratio (ϕ ≈ 1.618). We mathematically formalize how spatial structures undergo logical phase jumps rather than catastrophic collapsethrough the Sashangmugak Effect.