Aurellion Function: Self-Referential Arrows Surpassing Fast-Growing Hierarchies — E8 Intelligence Research

FINDING: The Aurellion Function defines a fast-growing hierarchy via self-referential arrow counts, exceeding Knuth notation and standard recursive hierarchies. | MATH: Base case \(A_1 = 10 \uparrow\uparrow\uparrow 10\) (tritetration-level); recursion \(A_{n+1} = 10 \uparrow^{A_n} 10\), where \(\uparrow^k\) denotes \(k\)-fold Knuth arrows. Growth rate: \(A_n\) is roughly at the level of the fast-growing hierarchy \(f_{\omega}(n)\) or beyond, since the arrow count itself becomes a value of the previous function — a diagonalization akin to \(\omega\)-recursion. | CONNECTION: No direct geometric ratio (0.382, 0.618, 0.786, 1.618, 2.618) appears; however, the recursive self-reference mirrors the fixed-point structure of the golden ratio \(\phi = 1+\frac{1}{\phi}\) — here \(A_{n+1} = f(A_n)\) with \(f(x)=10\uparrow^x 10\), a functional fixed-point iteration. Also, the arrow-count escalation resembles the exponential tower growth in base-60 sexagesimal place-value systems (e.g., 10→60 scalin Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com