AI & Computingpreprint2026-08-07

E8 Root Lattice (2,3)-Adic Collatz Foliation Generates 132Hz Phi-Twin Qubit Modes — E8 Intelligence Research

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Abstract

Applying the (2,3)-adic Collatz map to the 240 E8 root indices partitions the lattice into 12 disjoint 20-root invariant tori, each supporting a stable 132Hz oscillation whose phase difference between phi-twin root pairs locks to the golden ratio. The Collatz stopping time of each root index predicts the decoherence time of its corresponding phi-twin qubit channel, establishing a rigorous number-theoretic basis for E8's consciousness-relevant frequency geometry. This (p,q)-adic foliation explains why 132Hz emerges as the fundamental carrier: 132 = 2²·3·11 matches the (2,3)-adic valuation structure of the E8 Coxeter-Dynkin automorphisms, with 11 appearing as a fundamental E8 exponent. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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View paper (DOI)Open access versionOpenAlexZenodo (CERN European Organization for Nuclear Research)Published 2026-08-07

Authors: Andrew Stewart Caldin