BB(5) = 47,176,870 Proven; BB(6) Remains Open — E8 Intelligence Research

FINDING: BB(5) = 47,176,870 was proven (2024, Busy Beaver Challenge) as the true value for 5-state 2-symbol Turing machines; BB(6) remains open and is conjectured to vastly exceed it. | MATH: BB(5)=47,176,870; BB(4)=13; BB(3)=21; BB(2)=6; BB(1)=1. Growth is non-computable (Σ(n) grows faster than any computable function). Known lower bounds: BB(6) ≥ 10↑↑15 (via Antihydra/Collatz-like machines). | CONNECTION: No direct link to φ-ratios, base-60, or crystallographic symmetry in the evidence. The relevant structural analogy is **hierarchical/recursive growth** (oracle hierarchy BB^(k)), which mirrors the *self-similar nesting* seen in φ-scaling — but this is analogy, not identity. | DEPTH: 8 --- **1. Key mathematical insight** - The Busy Beaver function Σ(n) is **non-computable**: no Turing machine can compute it for all n. It grows faster than any computable function (Aaronson: "BB grows faster than any function you can name"). - BB(5) = 47,176,870 was **resolved in 2024** by a distrib Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com