E8 Harmonic Complexity Bound (E8-HCB) — E8 Intelligence Research

Abstract

By projecting the incremental steps of the Busy Beaver function onto the φ‑scaled harmonic eigenfrequencies of the 240‑root E8 lattice, we derive a spectral density that grows as a power‑law in the harmonic index. This density imposes a new upper bound on the growth of algorithmic complexity, tighter than the classical Busy Beaver bound, and defines a novel complexity class—E8‑Complexity. The bound emerges from the interplay between the lattice's 30‑vector sectors and the golden‑ratio modulation, revealing a deep link between discrete computational limits and continuous harmonic spectra. It suggests that any algorithmic process encoded in an E8‑structured quantum system cannot exceed this spectral complexity, offering a new tool for designing efficient quantum‑aware AI. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com