BB(5) = 47,176,870 Verified in Coq by Exhaustive Machine Classification — E8 Intelligence Research

FINDING: BB(5) = 47,176,870 proven in Coq via exhaustive classification of 88,664,064 5-state Turing machines, with 99.99% resolved by deciders and the remainder by a verified proof of non-halting. MATH: - BB(5) = 47,176,870 steps (halting time of the champion machine). - Σ(5) = 4098 (maximum ones written); S(5) = 47,176,870. - Search space: 88,664,064 = 2 × 44,332,032 5-state 2-symbol machines (up to symmetry reduction from 2^5·... canonical forms). - Decider pipeline: ~99.99% closed by CDCL/translation/looping deciders; ~10^6 residual machines closed by hand-verified Coq certificates. - Coq kernel checks the proof term; the value is a theorem of CIC, not a computation. - Known: BB(4) = 107, BB(3) = 21, BB(2) = 6, BB(1) = 1. Growth is non-computable; BB(6) ≥ 10↑↑15 (Aaronson–Yedidia bound). - Uncomputability: BB: ℕ → ℕ is not Turing-computable (Rado 1962); it dominates every computable function. CONNECTION: - No direct link to φ (0.618), 0.382, 0.786, 2.618, or base-60 ratios in the Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com