Abstract: We consider a scalar Euclidean QFT with interaction given by a bounded, measurable function V such that V± := limw → ±∞ V(w) exist. We find a field renormalization such that all the n-point connected Schwinger functions for n ≠ 2 exist non-perturbatively in the UV limit. They coincide with the tree-level one-particle irreducible Schwinger functions of the erf(ϕ/ √ 2) interaction with a coupling constant (V+ - V-)/2. By a slight modification of our construction we can change this coupling constant to (V+ - V-)/2., where V± := limw → 0± V(w). Thereby, non-Gaussianity of these latter theories is governed by a discontinuity of V at zero. The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/home-page