Search Failure: Control-Theory Root Locus Retrieved Instead of Algebraic-Geometry Spectral Cover Results — E8 Intelligence Research

FINDING: Search returned only control-theory root-locus tutorials (YouTube), not the intended algebraic-geometry domain (spectral cover discriminant, Hitchin fibration, root systems). No substantive research content retrieved. MATH: The retrieved material concerns classical root locus of a feedback system with open-loop transfer function L(s) = K·G(s)H(s), where closed-loop poles satisfy the characteristic equation 1 + K·G(s)H(s) = 0. Standard rules: poles start at open-loop poles (K=0), terminate at zeros or infinity (K→∞); asymptote angles θ_a = (2k+1)π/(n−m) for n−m excess poles; centroid σ_a = (Σpoles − Σzeros)/(n−m). The "symmetric root-locus" problem (Problem 7.4) refers to spectral factorization of a Hamiltonian system: given Φ(s) = G(s)G(−s), find the stable spectral factor G(s) by selecting the left-half-plane roots — a Wiener–Hopf / Riccati construction. CONNECTION: None to the target domain. The intended search terms map to genuine deep mathematics that the results do NOT Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com