Quantum Entanglement Decides Halting Problem: MIP* = RE Collapses Arithmetic Hierarchy — E8 Intelligence Research

FINDING: The MIP* = RE theorem collapses the classical arithmetic hierarchy at the level of quantum-verifiable problems, revealing that the halting problem is decidable by a quantum-entangled prover protocol. | MATH: MIP* = RE (multi-prover interactive proofs with quantum entanglement equal recursively enumerable sets); this implies the Connes embedding conjecture is false and the Tsirelson bound is non-closed; the quantum low-degree test replaces classical low-degree tests with entangled provers, yielding a gap between the classical Turing degree 0′ (halting problem) and the quantum-verifiable degree. | CONNECTION: The collapse is a *lattice-theoretic* phenomenon — the Turing degrees form a dense partial order; MIP* = RE forces the *join* of certain degrees to equal 0′, but the *meet* structure (via entanglement) is non-Archimedean. The quantum low-degree test uses *root-system-like* symmetries (Pauli groups, Clifford algebras) over finite fields, echoing crystallographic root lattice Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com