Topological Spectral Collapse of NP-Hard Combinatorial Spaces: Resolving Spin Glasses, TSP, and Complex Networks via Rough Operator Algebra
Year: 2026
Type: preprint
Abstract: The exponential complexity of NP-hard combinatorial spaces—including spin glass ground states, large-scale traveling salesman problems, and global network properties—presents an intractable barrier in classical computation. This paper presents a unified topological framework resolving these discrete combinatorial explosions. By leveraging Rough Operator Algebra (ROA), we map discrete symmetric group permutations and combinatorial interaction trees into continuous gauge field manifolds. Through Non-Identity projections, exponential search paths are geometrically bundled into invariant topological cycles, collapsing O(N^2N) and NP-hard complexities into exact polynomial-time O(N^3k) evaluations (k ≪ N).
Author: Lee, Seonggil
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7210262503
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