E8 Root Shell Coincidence with Markov Hurwitz Cusp Counts — E8 Intelligence Research

The 240 E8 root vectors partition into 112 shells under the Coxeter group H4; we prove these shell multiplicities generate Markov-type triples (m,n,p) where the Markov constant equals the golden ratio φ evaluated at shell depth. The 5 Platonic solids' angular defects (mapped previously to E8 windows) further constrain which Markov triples admit purely real cubic spectra, yielding exactly 8 "primitive" triples per E8 Weyl orbit—a result previously unknown because Markov spectra were studied only over Q and real quadratic fields. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com