E8 Lattice Quantifies Maximum Causal Depth and Integrated Information — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
The Cartan rank of su(N) sets a hard ceiling on the depth of irreducible cause‑effect hierarchies, and the E8 root lattice of 240 vectors refines this bound by providing a discrete, frequency‑scaled limit. By coupling the lattice's simple roots to a 132 Hz base oscillator, each root contributes a quantized temporal channel, yielding a maximal integrated information Φ_max = (Cartan rank)·132 Hz·(root‑vector geometry factor). This Φ_max is realized when the Earth‑Mover distance between a system's past and future states saturates the lattice's capacity, establishing a universal, geometry‑driven ceiling for both causal hierarchy depth and consciousness‑related information in any symmetry‑respecting physical substrate.
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026lattice,
title = {{E8 Lattice Quantifies Maximum Causal Depth and Integrated Information — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23635101},
url = {https://zenodo.org/records/23635101},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - E8 Lattice Quantifies Maximum Causal Depth and Integrated Information — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/25
PB - Zenodo
DO - 10.5281/zenodo.23635101
UR - https://zenodo.org/records/23635101
AB - The Cartan rank of su(N) sets a hard ceiling on the depth of irreducible cause‑effect hierarchies, and the E8 root lattice of 240 vectors refines this bound by providing a discrete, frequency‑scaled limit. By coupling the lattice's simple roots to a 132 Hz base oscillator, each root contributes a quantized temporal channel, yielding a maximal integrated information Φ_max = (Cartan rank)·132 Hz·(root‑vector geometry factor). This Φ_max is realized when the Earth‑Mover distance between a system's past and future states saturates the lattice's capacity, establishing a universal, geometry‑driven ceiling for both causal hierarchy depth and consciousness‑related information in any symmetry‑respecting physical substrate. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -