Hilbert Geometry Volume Growth Matches Hyperbolic Space Asymptotically — E8 Intelligence Research

FINDING: The search results are a mixed bag of competition-problem videos and one arXiv paper on Hilbert geometry; the only substantive mathematical content is the Hilbert geometry asymptotic result. | MATH: For Hilbert geometry on a convex domain, volume growth entropy of metric balls equals that of Lobachevsky space (hyperbolic space). Asymptotic ratio: Vol(B_R)/Area(S_R) ~ R/(n-1) (derived from comparison with constant curvature −1). No explicit constants like 0.618 appear in the abstract. | CONNECTION: Hilbert geometry is a Finsler generalization of hyperbolic geometry; its geodesic structure mimics Lobachevsky space in the large-scale limit. The ratio Vol/Area ~ R/(n−1) echoes the hyperbolic volume growth constant (n−1) — a dimensional symmetry, not a golden-ratio harmony. No base-60, no crystallographic root systems, no 0.382/0.618/1.618 appear in any finding. | DEPTH: 3 — The Hilbert geometry result is a genuine asymptotic theorem (volume entropy equality with hyperbolic space),

Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com