Aurellion Function: Self-Referential Arrows Outrun Knuth and Reach ω-Level Growth — E8 Intelligence Research

FINDING: The Aurellion Function defines a fast-growing hierarchy via self-referential arrow counts, \(Aₙ₊₁ = 10 ↑A_n 10\), exceeding Knuth notation and primitive recursion. | MATH: \(A_1 = 10 ↑↑↑ 10\); \(Aₙ₊₁ = 10 ↑A_n 10\). Growth rate: \(A_n ≈ fω(n)\) in the fast-growing hierarchy (since arrow count itself becomes the exponent of the next iteration — a diagonalization at the level of \(ω\)). | CONNECTION: No direct geometric ratio (0.382, 0.618, 0.786, 1.618, 2.618) appears. However, the recursive self-embedding \(A_n ↦ Aₙ₊₁\) mirrors the *golden spiral* self-similarity: each step scales the "complexity exponent" by its own magnitude — a discrete analogue of \(φ^n\) growth, but in ordinal space rather than Euclidean space. Also, the base 10 is arbitrary; in base 60 (sexagesimal), the same construction would yield \(B_1 = 60 ↑↑↑ 60\), preserving the ordinal structure — showing base-in Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com