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This work aims to redefine classical topology by introducing Seonggil Topology, focusing on discrete logic-based connections.

April 27, 2026Open Access

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

Key Points

This work aims to redefine classical topology by introducing Seonggil Topology, focusing on discrete logic-based connections.
Introduced a new framework, Seonggil Topology, derived from Rough Operator Algebra.
Mathematically formalized the concept of phase jumps in spatial structures.
Built on previous findings from SMT-Vol.1 and SMT-Vol.2.
Demonstrated that topological spaces can exist as discrete sets of logical states.
Found that spatial structures undergo logical phase jumps instead of catastrophic collapse through the Sashangmugak Effect.
Redefined smooth connectivity as unnecessary in topological analysis.

Abstract

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.

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

Key Points

Abstract

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