Algebraic Connectivity as a Key Spectral Measure in Hypercube Networks — E8 Intelligence Research

FINDING: Algebraic connectivity (second smallest Laplacian eigenvalue) is a key spectral measure for graph robustness, sparsification, and integrated information in hypercube topologies. | MATH: Algebraic connectivity λ₂ (Fiedler eigenvalue) of graph Laplacian L = D - A; for hypercube Q_n, λ₂ = 2 (constant, independent of dimension n); integrated information Φ related to spectral gap via Φ ∝ λ₂ / (λ_max - λ_min) in certain network models. | CONNECTION: Hypercube Q_n has eigenvalues λ_k = 2k for k=0..n, giving λ₂=2 exactly; ratio λ₂/λ_n = 2/(2n) = 1/n, which for n=3 yields 0.333 (close to 0.382 golden ratio complement), for n=5 yields 0.2 (related to 0.618/π?). No direct golden ratio or base-60 link evident. | DEPTH: 6 — solid mathematical result with applications to consciousness theory (integrated information theory uses hypercube topology), but no new constant or harmonic ratio discovered. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com