Hierarchical Multi-Scale Differential Topology (HMSDT): Resolution of High-Dimensional Pathologies via Advanced Rough Calculus and Non-Identity Spectral Collapse

The disparities between differential and topological structures—manifesting as exotic smooth structures in 4D, wild embeddings in Schoenflies problems, and complexities in high-dimensional classifications—are fundamentally emergent phenomena dependent on dimensional scale and resolution. By elevating the Hierarchical Multi-Scale Differential Topology (HMSDT) framework within the Unified Seonggil Frameworks (including ARC, Post Tensor Dynamics, and Non-Identity Calculus), we redefine smooth structures as dynamical phase states. Under this paradigm, classical 4D exotic phenomena [1] are subordinatedto specific roughness regimes, and high-dimensional spaces systematically converge to standard topological structures via Topological Spectral Collapse, completely bypassing classical non-constructive obstructions.