Quantum Entanglement Collapses Quantum Verification Hierarchy to Recursively Enumerable Class — E8 Intelligence Research

Abstract

FINDING: MIP*=RE proves quantum entanglement can verify undecidable problems, collapsing the quantum verification hierarchy into the classical recursively enumerable class. | MATH: MIP* = RE (where MIP* = multiprover interactive proofs with quantum entanglement, RE = recursively enumerable languages). The Halting Problem is in RE but not in R (decidable). This implies that the set of problems verifiable by entangled quantum provers is exactly the set of problems computable by a Turing machine that may not halt on non-members. | CONNECTION: No direct geometric ratios or constants (0.382, 0.618, etc.) appear. However, the result relies on the structure of the *commuting operator* model of quantum correlations, which is deeply tied to *operator algebras* and *C*-algebras — these have known connections to root systems and Lie algebras (e.g., the Weyl algebra, SU(2) representations). The proof uses a *self-testing* protocol based on the *linear constraint system* (LCS) games, which are buil Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com