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Every rigorous example so far is either free (no interaction) or lives in fewer dimensions.","posed_since":"","precise":"Construct a quantum field theory on $R^{(1,3)}$ satisfying the Wightman axioms (or Euclidean Osterwalder-Schrader axioms on $R^4$) whose truncated correlation functions are not all zero, i.e. a non-Gaussian theory with nontrivial scattering. Lattice $\\phi^4$ and Ising models in $d = 4$ give only Gaussian scaling limits, so candidates are asymptotically free theories such as Yang-Mills. Answer: an explicit construction with proof of the axioms and of non-Gaussianity.","problem_ref":null,"references":"","settled_by":"A refereed construction of one non-Gaussian Wightman or Osterwalder-Schrader theory in four dimensions.","status_note":"Aizenman and Duminil-Copin (Annals of Mathematics, 2021) proved that scaling limits of critical $4\\mathrm{D}$ Ising and lattice $\\phi^{4}$ models are Gaussian, removing the simplest candidate.","title":"Construct any interacting quantum field theory in four spacetime 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