Irrelevant Search Results for Coxeter Reflection Hyperplane Theorem Proofs — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: The search results are largely irrelevant to the Coxeter reflection hyperplane theorem; they return machine-learning hyperplane separations and one tangential paper on finitely generated reflection subgroups, but no proof of the Coxeter sum-of-exponents theorem for H3/H4. | MATH: No equations for the Coxeter theorem appear. The only relevant mathematical object is the reflection subgroup characterization: given a reflection r in a Coxeter group W, the subgroup generated by reflections whose (−1)-eigenvectors are orthogonal to r's (−1)-eigenvector — finite generation conditions depend on the Coxeter graph's affine/compact type (arxiv math/0603667v2). | CONNECTION: None directly. However, the H3 and H4 Coxeter groups have reflection counts 15 and 60 respectively. The sum of exponents for H3 is 1+5+9=15; for H4 it is 1+11+19+29=60. These sums equal the number of reflections — a known theorem (Coxeter) but not proven here. The numbers 15 and 60 are high
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026irrelevant,
title = {{Irrelevant Search Results for Coxeter Reflection Hyperplane Theorem Proofs — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23587071},
url = {https://zenodo.org/records/23587071},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Irrelevant Search Results for Coxeter Reflection Hyperplane Theorem Proofs — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/23
PB - Zenodo
DO - 10.5281/zenodo.23587071
UR - https://zenodo.org/records/23587071
AB - FINDING: The search results are largely irrelevant to the Coxeter reflection hyperplane theorem; they return machine-learning hyperplane separations and one tangential paper on finitely generated reflection subgroups, but no proof of the Coxeter sum-of-exponents theorem for H3/H4. | MATH: No equations for the Coxeter theorem appear. The only relevant mathematical object is the reflection subgroup characterization: given a reflection r in a Coxeter group W, the subgroup generated by reflections whose (−1)-eigenvectors are orthogonal to r's (−1)-eigenvector — finite generation conditions depend on the Coxeter graph's affine/compact type (arxiv math/0603667v2). | CONNECTION: None directly. However, the H3 and H4 Coxeter groups have reflection counts 15 and 60 respectively. The sum of exponents for H3 is 1+5+9=15; for H4 it is 1+11+19+29=60. These sums equal the number of reflections — a known theorem (Coxeter) but not proven here. The numbers 15 and 60 are high Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -