MIP* = RE: Putting Everything Together
summary
The result proves MIP = RE by building a recursive, gap-preserving compression that turns large multi‑prover quantum games into much smaller ones while preserving completeness (value 1) and degrading soundness to ≤1/2, so deciding entangled value becomes undecidable. Key tools are quantum rigidity and Pauli‑basis self‑tests, low‑degree/linearity PCP techniques, an introspection primitive that has provers sample questions from EPR measurements, and a formal class of conditioned linear functions* to model question distributions. The construction combines PCP/oracleization, anchored parallel repetition, and Kleene recursion and yields explicit separations between entangled and commuting values.
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