Arithmetical Hierarchy Mirrors A∞ Root System in Lattice QCD Mass Extraction — E8 Intelligence Research

FINDING: The arithmetical hierarchy defines a countable ladder of undecidability (Σₙ/Πₙ), while lattice QCD links discrete symmetry-breaking to heavy-quark mass extraction. | MATH: Σₙ₊₁ = {x : ∃y R(x,y), R ∈ Πₙ}; Πₙ = co-Σₙ; Δₙ = Σₙ ∩ Πₙ. Turing jump: ∅⁽ⁿ⁾ is Σₙ-complete. Lattice QCD: m_Q from correlators G(t) = Σₙ |⟨0|J|n⟩|² e^(−Eₙt), with Eₙ = m_Q + binding, on a hypercubic lattice with spacing a. | CONNECTION: The arithmetical hierarchy's structure mirrors a **root system of type A∞** — each level Σₙ/Πₙ is a node, with the Turing jump as a simple root raising rank. Lattice QCD uses **hypercubic (Z⁴) symmetry**, a crystallographic point group (order 384), whose irreducible representations classify meson states — a direct base‑60-free but **lattice‑harmonic** decomposition. No golden‑ratio constants appear; the hierarchy is discrete, not continuous. | DEPTH: 6 — profound in logic (Turing degrees form a dense partial order, but the arithmetical ladder is a countable skeleton), and in p Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com