Remark on the existence of 44

The bound |Sε(2)g)|<~const|f|S|g|S, uniform as the lattice spacing ε→0, is sufficient to yield construction of a 4 field theory. In perturbation theory, this bound holds in spacetime dimensions d<~4. The bounds on the n-point Schwinger functions follow from the given bound by the use of Lebowitz's inequalities. They yield the growth |S(n)|<~O(n!), consistent with the Osterwalder-Schrader axioms, which allow reconstruction of a real-time theory.