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An Explicit Polynomial Counterexample to Connes' Embedding Conjecture
We construct an explicit Hermitian polynomial $ f $ with integer coefficients, of degree $ 12 $ in $ 65 $ selfadjoint variables, whose normalized trace is at least $3/4$ on every tuple of selfadjoint matrix contractions, in every dimension, and equals $-1$ at a specified tuple of selfadjoint unitari
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