Irrelevant Search Results for Coxeter Reflection Hyperplane Theorem Proofs — E8 Intelligence Research

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