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The limit should be interacting, not a free theory.","posed_since":"","precise":"Take $\\mathrm{SU}(N)$ lattice gauge theory with the Wilson action on $(\\epsilon \\mathrm{Z})^4$, with bare coupling chosen by asymptotic freedom, $g(\\epsilon)^2 \\sim 1/(2 b_0 \\log(1/(\\epsilon \\Lambda)))$ with $b_0 = 11 N/(48 \\pi^2)$, i.e. $1/g^2 \\sim (11 N/(24 \\pi^2)) \\log(1/(\\epsilon \\Lambda))$. Prove that correlations of gauge-invariant observables (smoothed Wilson loops or smeared $F^2$) converge as $\\epsilon \\to 0$ in infinite volume to a non-Gaussian limit satisfying the Osterwalder-Schrader axioms. Answer: a proof.","problem_ref":"59f5a39798c9d34582c88fc7916969379ec1acf473ca0f0f75f8a3d2b3c5ff26","references":"","settled_by":"A rigorous renormalization-group or probabilistic proof of the infinite-volume continuum limit with non-Gaussian correlations.","status_note":"Balaban's renormalization-group program of the 1980s gave ultraviolet stability bounds in finite volume but did not complete the construction.","title":"Continuum limit of four-dimensional lattice Yang-Mills 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