Absence of Direct Evidence for B_n/C_n Invariant Degree Identity in Search Results — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
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,…,2n. The root length ratio (long/short) is √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{ℓ(x)+ℓ(y)−ℓ(w) | w=xy, x2=y2=1}.
CONNECTION: The √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
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BibTeX
@misc{caldin2026absence,
title = {{Absence of Direct Evidence for B_n/C_n Invariant Degree Identity in Search Results — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23587238},
url = {https://zenodo.org/records/23587238},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Absence of Direct Evidence for B_n/C_n Invariant Degree Identity in Search Results — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/23
PB - Zenodo
DO - 10.5281/zenodo.23587238
UR - https://zenodo.org/records/23587238
AB - 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,…,2n. The root length ratio (long/short) is √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{ℓ(x)+ℓ(y)−ℓ(w) | w=xy, x^2=y^2=1}. CONNECTION: The √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
ER -