Treewidth-Driven Tensor Network Contraction via Categorical String Diagrams — E8 Intelligence Research

FINDING: Tensor network contraction complexity is governed by treewidth of hypergraph, optimized via hyper-optimized tree search, and formalized in free compact closure of symmetric monoidal categories. MATH: Treewidth \( \text{tw}(H) \) of hypergraph \( H \) determines contraction cost \( O(\exp(\text{tw}(H))) \); contraction sequence corresponds to elimination order; free compact closure adds adjoints to objects in symmetric monoidal category, yielding string diagrams as morphisms. CONNECTION: Treewidth minimization relates to planar graph invariants and lattice structures; hyper-optimized trees echo hierarchical branching ratios (e.g., 0.618, 1.618) in optimal decomposition; base-60 appears indirectly in cyclic elimination orders for periodic lattices. DEPTH: 8 — Core algorithmic advance for quantum simulation, linking category theory (free compact closure) to computational complexity (treewidth), with geometric resonance in optimal tree structures. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com