 Constructive QFT is an attempt to mediate between LQFT and axiomatic QFT by rigorously constructing specific interacting models of QFT. The nontrivial solutions it constructs are supposed to correspond to Lagrangians that particle physicists use. This ensures that various axiomatic systems have a physical connection to the world via the empirical success of LQFT. While constructive QFT has done this for some models with dimensions less than 4, it has not yet been accomplished for a 4 dimensional Lagrangian that particle physicists use. Any model that satisfies the Osterwalder-Schrader axioms will automatically satisfy the Wightman axioms. Constructive QFT tries to construct the functional integral measures for path integrals by shifting from Minkowski spacetime to Euclidean spacetime via a Wick rotation (what follows is based on section four of Hancox-Li (2017)). In Euclidean field theory, the Schwinger functions, which are defined in terms of \(Z\), must satisfy the Osterwalder-Schrader axioms. The measure of \(Z\) is a Gaussian measure on the Schwartz space of rapidly decreasing functions. The Osterwalder-Schrader axioms are related to the Wightman axioms by the Osterwalder-Schrader Reconstruction Theorem which states that any set of functions satisfying the Osterwalder-Schrader axioms determines a unique Wightman model whose Schwinger functions form that set. It allows the constructive field theorists to use the advantages of Euclidean space for defining a measure while ensuring that they are constructing models that exist in Minkowski spacetime. It still has to be verified that the solution corresponds to a renormalized perturbation series that physicists derive for the corresponding Lagrangian in LQFT. The challenge is how to translate something not mathematically well-defined into something that is while showing that the “solutions” in LQFT can be reproduced by something that is consistent with a set of axioms. This is crucial since, as Swanson (2017) points out, it is unclear whether perturbation theory is an accurate guide for the underlying physics described by LQFT. This leads Hancox-Li (2017) to argue that mathematically unrigorous LQFT is relevant to the rigorous program of constructive QFT in building rigorous interacting models of QFT. Those models correspond to the Lagrangians of interest to particle physicists. Hence, LQFT can inform the theoretical content of QFT.