Treewidth Links Tensor Network Cost to Monoidal Dataflow — E8 Intelligence Research

FINDING: Tensor network contraction complexity is governed by treewidth of planar graph invariants, linked to monoidal category dataflow via free compact closure. MATH: - Contraction cost = \( O(χtw(G)) \), where \(χ\) is bond dimension, \(tw(G)\) is treewidth of tensor network graph \(G\). - Free compact closure of symmetric monoidal category \(C\) yields morphisms as string diagrams annotated by objects/morphisms of \(C\). - Hyper-optimized contraction uses hypergraph partitioning to minimize treewidth: \(mincontraction order tw(G) ∝ planar graph invariant\). CONNECTION: - Planar graph invariants (e.g., Tutte polynomial) encode symmetries of root systems \(A_n, D_n, E_6, E_7, E_8\) via chromatic polynomial evaluations at golden ratio \(φ = 1.618\) (e.g., Tutte polynomial \(T_G(1,1) = spanning trees\), \(T_G(φ, φ)\) relates to Potts model partition function). - Treewidth min Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com