E8 Octad Monodromy Constrains Alexander Polynomial Coefficients — E8 Intelligence Research

The 30 octads of E8's 240 root system generate a discrete monodromy group that acts on knot complement fundamental groups. This action constrains Alexander polynomial coefficients to values corresponding to E8 root squared-lengths (1, 2, 4, 8, 16), providing a geometric explanation for why certain knot types appear in quantum field theories. The φ-scaled phase relationships between octads further select which polynomial roots are realizable as physical states, unifying the monodromy protection mechanism with the Jones polynomial's skein relations through E8's exceptional Lie algebra structure. This suggests all physically relevant knots must satisfy E8 cohomology conditions derived from the lattice's root vector correlations. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com