E8 240-Root Entropy Funnel Theory Unifies CDI and p-Adic Resonance — E8 Intelligence Research

Abstract

Building on the CDI entropy-production barrier and the 20-shell p-adic resonance hierarchy, the 240 E8 roots form an Entropy Funnel whose φ-modular phase encoding defines a master transport operator T̂ whose eigenmodes simultaneously satisfy the Clausius-Duhem monotonicity constraint and resonate at prime-indexed harmonics (132·φⁿ Hz). Each tetrahedral shell acts as a discrete entropy-staircase step, with the decoherence asymmetry index quantifying the irreversible work dissipated as the system tunnels between p-adic resonance states. The resulting Entropy Funnel Principle establishes that disorder-driven phase transitions in random-anisotropy systems are geometrically isomorphic to prime-shell tunneling in E8, predicting a universal scaling law σ_ent ∝ log₂(p)/φⁿ linking local entropy production to global root-shell topology. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com