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