E8 Root-Phase Conservation Bounds Effective Causal Depth — E8 Intelligence Research

An irreducible causal step requires a nonzero transition between E8 root states; transitions summing to zero form closed lattice cycles and add no causal depth. Assigning a 132 Hz reference to the lattice and φ-coupling adjacent modes makes effective depth equal to the rank of the smallest E8 face spanned by active roots, tightening the absolute Cartan-rank ceiling. Maximal depth therefore requires an open path through linearly independent roots, whereas φ-resonant cycles produce mode locking instead of deeper causation. This predicts a measurable transition from hierarchical dynamics to closed beat patterns at the active-face rank.

Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com