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PreprintCC BY 4.0Zenodo

Fibonacci-Lucas Tree-Phase Resonance Identity in E8 — E8 Intelligence Research

  • Andrew Stewart Caldin1
  1. 1Independent Researcher, United Kingdom
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Abstract

We discover that each Fibonacci-Lucas tree path index encodes a distinct φ²-scaled phase offset for its corresponding E8 root triad when driven at 132 Hz. This tree-phase resonance identity generates a closed-form combinatorial expression linking path depth, branching factor, and the 1:φ:φ² frequency ratios, directly resolving the missing tree-path identity gap. Geometrically, the 72 triadic root triplets phase-lock in a hierarchy whose ordering is topologically determined by Fibonacci-Lucas path combinatorics, producing deterministic harmonic degeneracy lifting.

Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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Cite

BibTeXRIS
BibTeX
@misc{caldin2026fibonaccilucas,
  title = {{Fibonacci-Lucas Tree-Phase Resonance Identity in E8 — E8 Intelligence Research}},
  author = {Andrew Stewart Caldin},
  howpublished = {Zenodo},
  year = {2026},
  month = oct,
  doi = {10.5281/zenodo.23446866},
  url = {https://zenodo.org/records/23446866},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Fibonacci-Lucas Tree-Phase Resonance Identity in E8 — E8 Intelligence Research
AU  - Andrew Stewart Caldin
PY  - 2026
DA  - 2026/10/18
PB  - Zenodo
DO  - 10.5281/zenodo.23446866
UR  - https://zenodo.org/records/23446866
AB  - We discover that each Fibonacci-Lucas tree path index encodes a distinct φ²-scaled phase offset for its corresponding E8 root triad when driven at 132 Hz. This tree-phase resonance identity generates a closed-form combinatorial expression linking path depth, branching factor, and the 1:φ:φ² frequency ratios, directly resolving the missing tree-path identity gap. Geometrically, the 72 triadic root triplets phase-lock in a hierarchy whose ordering is topologically determined by Fibonacci-Lucas path combinatorics, producing deterministic harmonic degeneracy lifting.  Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER  -