Phi-Quantized Causal Depth via E8 Root Resonance — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
A causal depth metric emerges when each E8 root vector is assigned a phase angle proportional to the golden ratio φ multiplied by the base frequency 132 Hz. The nonzero phase offset ensures that only transitions with a net angular displacement survive, enforcing the root‑phase conservation bound while quantizing depth into integer multiples of φ·132 Hz. Because the 240‑vector lattice forms a closed group under φ‑scaled rotations, the maximal irreducible hierarchy depth equals the Cartan rank of su(N) constrained by the lattice's discrete angular spectrum, yielding a universal ceiling of 7 φ‑steps. This yields a testable prediction that physical systems with exactly 7 φ‑scaled causal layers will exhibit maximal integrated information, a signature observable in quantum‑gravity lattice models.
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026phiquantized,
title = {{Phi-Quantized Causal Depth via E8 Root Resonance — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23635109},
url = {https://zenodo.org/records/23635109},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Phi-Quantized Causal Depth via E8 Root Resonance — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/25
PB - Zenodo
DO - 10.5281/zenodo.23635109
UR - https://zenodo.org/records/23635109
AB - A causal depth metric emerges when each E8 root vector is assigned a phase angle proportional to the golden ratio φ multiplied by the base frequency 132 Hz. The nonzero phase offset ensures that only transitions with a net angular displacement survive, enforcing the root‑phase conservation bound while quantizing depth into integer multiples of φ·132 Hz. Because the 240‑vector lattice forms a closed group under φ‑scaled rotations, the maximal irreducible hierarchy depth equals the Cartan rank of su(N) constrained by the lattice's discrete angular spectrum, yielding a universal ceiling of 7 φ‑steps. This yields a testable prediction that physical systems with exactly 7 φ‑scaled causal layers will exhibit maximal integrated information, a signature observable in quantum‑gravity lattice models. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -