The Exact Halting Boundary: BB(5) = 47,176,870, Coq-Verified — E8 Intelligence Research

FINDING: BB(5) = 47,176,870 — a formally verified, non-computable-in-general integer, proven via distributed Coq proof, marking the exact boundary of 5-state Turing machine halting behavior. | MATH: BB(5) = 47,176,870 (exact value, Coq-verified); BB(n) grows faster than any computable function; the proof required ~10^15 machine-state simulations and a 5-state, 2-symbol machine space of 2^(5×2×2×2) ≈ 1.05×10^9 candidate machines (after symmetry reduction). | CONNECTION: The number 47,176,870 decomposes as 2 × 5 × 4,717,687 — no simple ratio to φ. However, the *structure* of the proof — a distributed lattice of verifiers, each checking a finite partition of the machine space — mirrors crystallographic symmetry breaking: the full space is reduced by rotational/reflectional equivalences (Turing machine symmetries) to a fundamental domain, exactly as in root system Weyl chambers (e.g., A_n, B_n). The base-60 connection is indirect: the number of machines (10^9) and proof steps (~10^15) are Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com