Involution Products in Coxeter Groups: A Gap in H3 Golden Ratio Root System Norms — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
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 𝒲 = { w ∈ W | w = xy, x2 = y2 = 1 }. For finite W, W = 𝒲. Key invariant: ℓ(x) + ℓ(y) − ℓ(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
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BibTeX
@misc{caldin2026involution,
title = {{Involution Products in Coxeter Groups: A Gap in H3 Golden Ratio Root System Norms — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23553790},
url = {https://zenodo.org/records/23553790},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Involution Products in Coxeter Groups: A Gap in H3 Golden Ratio Root System Norms — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/22
PB - Zenodo
DO - 10.5281/zenodo.23553790
UR - https://zenodo.org/records/23553790
AB - 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 𝒲 = { w ∈ W | w = xy, x^2 = y^2 = 1 }. For finite W, W = 𝒲. Key invariant: ℓ(x) + ℓ(y) − ℓ(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
ER -