In minimal surface theory, the ability to approximate an unknown object by objects with quantitative derivative controls, is frequently the key of the regularity theory. Notable examples include the Lipschitz and harmonic approximations that lie at the core of De Giorgi’s $\epsilon$-regularity theorem, and the center manifolds at the core of Almgren’s big regularity theorem. An excellent survey is [25]. While there are plenty of techniques for constructing area competitors in geometric measure theory, we lack useful ways to construct competitors within the Lagrangian world. Developing such techniques is essential to the $L^{p}$-smoothing property, and possibly also to the Floer theoretic aspects of the variational program.