Absence of Direct Evidence for B_n/C_n Invariant Degree Identity in Search Results — E8 Intelligence Research

FINDING: The search results are largely tangential video lectures and one arXiv paper on Coxeter group excess; no direct source addresses the B_n/C_n invariant degree identity or root length ratio. The arXiv paper (1405.2700) defines excess for strongly real elements in finite Coxeter groups, but does not compare B_n vs C_n degrees. MATH: No new equations or constants extracted. The relevant known fact (not in results, but standard): For B_n and C_n, the Weyl group is the same hyperoctahedral group, with invariant degrees \(2,4,6,\dots,2n\). The root length ratio (long/short) is \(\sqrt{2}\) for B_n vs C_n (when normalized), but the group structure is identical — hence identical degree sequences. The paper's excess function: \(e(w)=\min\{\ell(x)+\ell(y)-\ell(w) \mid w=xy, x^2=y^2=1\}\). CONNECTION: The \(\sqrt{2}\) ratio appears in the root length difference between B_n (long roots) and C_n (short roots) — but since the Weyl group is the same, this ratio does not alter the invariant

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