Golden-Ratio Metric Tensor and H3 Invariants: A Search Gap in Coxeter Literature — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Search results are mostly pedagogical videos on metric tensors and Coxeter groups, with one relevant arXiv paper on involution products in Coxeter groups — no direct H3 invariant-degree or golden-ratio metric tensor content surfaced. | MATH: No explicit equations for H3 invariants (2,6,10) or golden-ratio metric tensor appear in the results. The arXiv paper (1405.3051) concerns finite Coxeter groups where every element is a product of two involutions, with a defect function ℓ(x)+ℓ(y)−ℓ(w) minimized; no specific H3 or φ values stated. | CONNECTION: Indirect — H3 (icosahedral symmetry) is known to have invariant degrees 2, 6, 10 and its Coxeter number is 10; the golden ratio φ = (1+√5)/2 ≈ 1.618 appears in H3's root system norms and in the icosahedron's geometry. However, the search results do not explicitly link φ to a metric tensor. Crystallographic symmetry is mentioned only via the German video on metric tensors in crystal systems, but no H3 (non-crystallographic) connection
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026goldenratio,
title = {{Golden-Ratio Metric Tensor and H3 Invariants: A Search Gap in Coxeter Literature — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23658551},
url = {https://zenodo.org/records/23658551},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Golden-Ratio Metric Tensor and H3 Invariants: A Search Gap in Coxeter Literature — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/26
PB - Zenodo
DO - 10.5281/zenodo.23658551
UR - https://zenodo.org/records/23658551
AB - FINDING: Search results are mostly pedagogical videos on metric tensors and Coxeter groups, with one relevant arXiv paper on involution products in Coxeter groups — no direct H3 invariant-degree or golden-ratio metric tensor content surfaced. | MATH: No explicit equations for H3 invariants (2,6,10) or golden-ratio metric tensor appear in the results. The arXiv paper (1405.3051) concerns finite Coxeter groups where every element is a product of two involutions, with a defect function ℓ(x)+ℓ(y)−ℓ(w) minimized; no specific H3 or φ values stated. | CONNECTION: Indirect — H3 (icosahedral symmetry) is known to have invariant degrees 2, 6, 10 and its Coxeter number is 10; the golden ratio φ = (1+√5)/2 ≈ 1.618 appears in H3's root system norms and in the icosahedron's geometry. However, the search results do not explicitly link φ to a metric tensor. Crystallographic symmetry is mentioned only via the German video on metric tensors in crystal systems, but no H3 (non-crystallographic) connection Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -