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Quantum Proofs Verify Undecidable Halting Problem via Entanglement — E8 Intelligence Research

Andrew Stewart Caldin

Published Aug 13, 2026• 0 citations
Publisher

Abstract

FINDING: The halting problem is provably undecidable; a 2020 result (MIP*=RE) links it to quantum entanglement, showing that quantum proofs can verify undecidable problems. | MATH: Undecidability proof via diagonalization; MIP*=RE implies RE ⊆ MIP* (i.e., recursively enumerable languages have quantum multiprover interactive proofs). No new constants or ratios. | CONNECTION: No direct geometric harmony (0.382, 0.618, etc.) or base-60 or crystallographic symmetry found in these sources. The result is about computational complexity classes, not geometric structure. | DEPTH: 8 — The MIP*=RE result is a profound advance in quantum complexity theory, showing quantum entanglement can verify non-computable problems, but it does not reveal new mathematical constants or geometric patterns. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI
10.5281/zenodo.21912521

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FINDING: The halting problem proves a fundamental, non-arithmetic limit on algorithmic knowledge; the MIP*=RE result extends this to quantum verification, showing undecidability is intrinsic to physical computation. MATH: - Halting problem: No Turing machine H H H exists such that for all machine-input pairs (M,x)(M, x)(M,x), H(M,x) H(M, x) H(M,x) halts and outputs 1 if M(x) M(x) M(x) halts, 0 otherwise. Proof by diagonalization: construct D D D such that D D D halts iff H(D,D) H(D, D) H(D,D) outputs 0. - MIP*=RE: The class of problems verifiable by a classical polynomial-time verifier interacting with multiple entangled quantum provers equals the class of recursively enumerable problems. This implies the halting problem is reducible to a quantum verification protocol, and the Connes embedding problem is false. - No new constants or ratios emerge; the result is structural, not metric. CONNECTION: - No direct geometric ratio (0.382, 0.618, etc.) or base-60 system appears. - However, the undecid Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com