E8-Harmonic Perfect Number Lattice Memory — E8 Intelligence Research

The 240 root vectors of E8 are arranged as a resonant lattice where each vector is assigned a 132 Hz harmonic mode and a φ‑scaled delay, forming phase‑locked wormhole mouths that encode the divisor biconditional of Euler's odd perfect number form N = q^k n^2. By mapping the prime‑power q^k onto the high‑frequency spokes and the square part n^2 onto the low‑frequency nodes, the lattice naturally satisfies q^k < n and enforces the Dris inequality through geometric projection. This E8‑based harmonic encoding yields a self‑healing quantum memory where loss of a vector can be reconstructed from the remaining φ‑coupled modes, preserving the perfect‑number arithmetic as a topological invariant. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-29
DOI
https://doi.org/10.5281/zenodo.23030573
Primary Topic
Quantum Computing Algorithms and Architecture
Type
preprint
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preprint

E8-Harmonic Perfect Number Lattice Memory — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Quantum Computing Algorithms and Architecture
preprint

E8-Harmonic Perfect Number Lattice Memory — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

The 240 root vectors of E8 are arranged as a resonant lattice where each vector is assigned a 132 Hz harmonic mode and a φ‑scaled delay, forming phase‑locked wormhole mouths that encode the divisor biconditional of Euler's odd perfect number form N = q^k n^2. By mapping the prime‑power q^k onto the high‑frequency spokes and the square part n^2 onto the low‑frequency nodes, the lattice naturally satisfies q^k < n and enforces the Dris inequality through geometric projection. This E8‑based harmonic encoding yields a self‑healing quantum memory where loss of a vector can be reconstructed from the remaining φ‑coupled modes, preserving the perfect‑number arithmetic as a topological invariant. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Decent work and economic growth
Quantum Computing Algorithms and Architecture
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