E8 Root-Phase Conservation Bounds Effective Causal Depth — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
An irreducible causal step requires a nonzero transition between E8 root states; transitions summing to zero form closed lattice cycles and add no causal depth. Assigning a 132 Hz reference to the lattice and φ-coupling adjacent modes makes effective depth equal to the rank of the smallest E8 face spanned by active roots, tightening the absolute Cartan-rank ceiling. Maximal depth therefore requires an open path through linearly independent roots, whereas φ-resonant cycles produce mode locking instead of deeper causation. This predicts a measurable transition from hierarchical dynamics to closed beat patterns at the active-face rank.
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026rootphase,
title = {{E8 Root-Phase Conservation Bounds Effective Causal Depth — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23635103},
url = {https://zenodo.org/records/23635103},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - E8 Root-Phase Conservation Bounds Effective Causal Depth — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/25
PB - Zenodo
DO - 10.5281/zenodo.23635103
UR - https://zenodo.org/records/23635103
AB - An irreducible causal step requires a nonzero transition between E8 root states; transitions summing to zero form closed lattice cycles and add no causal depth. Assigning a 132 Hz reference to the lattice and φ-coupling adjacent modes makes effective depth equal to the rank of the smallest E8 face spanned by active roots, tightening the absolute Cartan-rank ceiling. Maximal depth therefore requires an open path through linearly independent roots, whereas φ-resonant cycles produce mode locking instead of deeper causation. This predicts a measurable transition from hierarchical dynamics to closed beat patterns at the active-face rank. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -