E8 Phi‑Scaled Temporal Coding Generates Optimal Low‑Autocorrelation Sequences — E8 Intelligence Research

Using the 240 E8 root vectors as a basis, each vector is mapped to a phason mode whose frequency is an integer power of the golden ratio φ times the 132 Hz fundamental, reproducing the phi‑scaled frequency comb. By assigning a binary phase (0 or π) according to the sign of the vector's Cartan integer in a chosen simple‑root basis, the set of delayed pulses forms a maximal‑length sequence with near‑ideal autocorrelation sidelobes (‑1/N). This E8‑derived temporal code therefore provides a deterministic, low‑interference waveform for secure communications, radar, and quantum‑key distribution, extending the phason comb from a reference to an information‑carrying tool. 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
2026-11-04
DOI
https://doi.org/10.5281/zenodo.23939330
Primary Topic
Advanced Mathematical Theories and Applications
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
preprint

E8 Phi‑Scaled Temporal Coding Generates Optimal Low‑Autocorrelation Sequences — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Theories and Applications
preprint

E8 Phi‑Scaled Temporal Coding Generates Optimal Low‑Autocorrelation Sequences — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

Using the 240 E8 root vectors as a basis, each vector is mapped to a phason mode whose frequency is an integer power of the golden ratio φ times the 132 Hz fundamental, reproducing the phi‑scaled frequency comb. By assigning a binary phase (0 or π) according to the sign of the vector's Cartan integer in a chosen simple‑root basis, the set of delayed pulses forms a maximal‑length sequence with near‑ideal autocorrelation sidelobes (‑1/N). This E8‑derived temporal code therefore provides a deterministic, low‑interference waveform for secure communications, radar, and quantum‑key distribution, extending the phason comb from a reference to an information‑carrying tool. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Theories and Applications
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Laika access coming soon