PreprintCC BY 4.0Zenodo
Fractal Z₂ Invariant Tower via Recursive TRIM Berry Phases — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
The eight phi-scaled E8 resonance shells induce a recursive Berry connection where the TRIM parity product of shell *n* becomes the Berry phase defining the Z₂ invariant of shell *n*+1. This generates a fractal tower of topological invariants — each level holographically encoding the full nesting structure — which quantizes inter-shell coupling into discrete phi-harmonic ratios. The resulting meta-invariant protects coherent quantum transport across all 132Hz phi-scaled bandwidths simultaneously, predicting experimentally measurable fractional Josephson frequencies at phi⁻ᵏ multiples of the base gap.
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026fractal,
title = {{Fractal Z₂ Invariant Tower via Recursive TRIM Berry Phases — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23447007},
url = {https://zenodo.org/records/23447007},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fractal Z₂ Invariant Tower via Recursive TRIM Berry Phases — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/18
PB - Zenodo
DO - 10.5281/zenodo.23447007
UR - https://zenodo.org/records/23447007
AB - The eight phi-scaled E8 resonance shells induce a recursive Berry connection where the TRIM parity product of shell *n* becomes the Berry phase defining the Z₂ invariant of shell *n*+1. This generates a fractal tower of topological invariants — each level holographically encoding the full nesting structure — which quantizes inter-shell coupling into discrete phi-harmonic ratios. The resulting meta-invariant protects coherent quantum transport across all 132Hz phi-scaled bandwidths simultaneously, predicting experimentally measurable fractional Josephson frequencies at phi⁻ᵏ multiples of the base gap. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -