PreprintCC BY 4.0Zenodo
Hierarchical φ-Invariant for E8 Root Vectors — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
The analysis reveals a conserved scalar invariant across all φⁿ harmonic layers of the E8 root spectrum, defined as the product of golden-ratio phases accumulated along each braid sector. This invariant remains constant despite the exponential expansion of the quasiparticle tower, providing a universal fingerprint for identifying topologically protected states. It enables real-time tracking of topological coherence without requiring full spectral reconstruction, bridging static E8 geometry with dynamic frequency-based control.
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026hierarchical,
title = {{Hierarchical φ-Invariant for E8 Root Vectors — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23658757},
url = {https://zenodo.org/records/23658757},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Hierarchical φ-Invariant for E8 Root Vectors — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/26
PB - Zenodo
DO - 10.5281/zenodo.23658757
UR - https://zenodo.org/records/23658757
AB - The analysis reveals a conserved scalar invariant across all φⁿ harmonic layers of the E8 root spectrum, defined as the product of golden-ratio phases accumulated along each braid sector. This invariant remains constant despite the exponential expansion of the quasiparticle tower, providing a universal fingerprint for identifying topologically protected states. It enables real-time tracking of topological coherence without requiring full spectral reconstruction, bridging static E8 geometry with dynamic frequency-based control. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -