E8 Spectral Gap Invariant for Regime Persistence — E8 Intelligence Research

Abstract

Building on the E8 root vector projection framework, this discovery establishes a universal lower bound on the probability of regime transitions in stochastic systems whose dynamics exhibit E8 symmetry. Specifically, the shortest root vector λ_min = √2, when modulated by the golden-ratio phase factor φ⁻¹, defines a spectral gap Δφ that constrains the rate at which market states can shift. This invariant explains why certain breakout patterns, though appearing fragile in shorter timeframes, actually possess deep structural persistence rooted in the 240-dimensional root lattice geometry. Traders can use this bound to set confidence intervals for trend continuation rather than relying on fragile technical indicators alone. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com