Involution Products in Coxeter Groups: A Gap in H3 Golden Ratio Root System Norms — E8 Intelligence Research

FINDING: The search results are predominantly pedagogical videos and a single arXiv paper on involution products in Coxeter groups — none specifically address H3, golden ratio root systems, or norm calculations. The arXiv paper (1405.3051) is the only substantive mathematical content, dealing with involution products in general Coxeter groups. MATH: The paper defines \(\mathcal{W} = \{ w \in W \;|\; w = xy, \; x^2 = y^2 = 1 \}\). For finite \(W\), \(W = \mathcal{W}\). Key invariant: \(\ell(x) + \ell(y) - \ell(w)\), minimized over all such factorizations. No explicit golden ratio, no H3-specific norm, no root system coordinates appear in the abstract. CONNECTION: None directly. The paper is general Coxeter theory, not H3. The videos are expository (classification, representation theory, geometric realization) — they may *contain* H3 examples, but no extractable equations or constants are provided in the search snippets. No 0.382, 0.618, 0.786, 1.618, 2.618, or base-60 appear. DEPTH:

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