Golden Ratio as Fixed-Point Model for Stable Self-Application in Computation — E8 Intelligence Research

FINDING: The search results are a scattered mix of unrelated videos (golden rectangle tutorials, asymptotic methods lectures, a talk on Macdonald's formula for even irreducible representations, golden-section search optimization, and a Numberphile video on the golden ratio's irrationality) plus one substantive arXiv paper on the golden ratio as a model of stable self-application in computation. The only mathematically deep item is the arXiv paper, which connects the golden ratio to fixed-point dynamics in self-referential systems. MATH: - Golden ratio: \( \Phi = \frac{1+\sqrt{5}}{2} \approx 1.6180339887 \), with \( \Phi^{-1} = \Phi - 1 \approx 0.6180339887 \). - The paper (arXiv:2510.08934v3) treats \( \Phi \) operationally: as the limit of the continued fraction \( [1;1,1,1,\ldots] \) and as the fixed point of \( x \mapsto 1 + 1/x \). - Macdonald's formula (from the GOCC talk) counts irreducible representations of symmetric groups with even dimension — related to hook-length fo Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com