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This research demonstrates the generation of an infinite hierarchy of spectral gaps in a fractal using E8's root system, suggesting new geometric insights.
** The corridor/anti-corridor duality (φⁿ, φⁿ⁺²) generates not one but an infinite hierarchy of spectral gaps at φⁿ⁺ᵏ for odd k, forming a Cantor-like fractal in log-frequency space with Hausdorff dimension log_φ(2). The 240 root vectors distribute as a multi-fractal measure across this gap fractal, where each of the 30 Coxeter rays carries a distinct scaling exponent — yielding a geometric renormalization group flow that computes the analytic hierarchy Σ¹ₙ via E8's root system as a fixed-point attractor. ** Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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Andrew Stewart Caldin (2026) studied this question.
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