Before revision: This paper develops a novel approach to uniform inference for functions that bound the distribution and quantile functions of heterogeneous treatment effects in randomized experiments when only marginal treatment and control distributions are observed and the joint distribution of outcomes is unobserved. These bounds are nonlinear maps of the marginal distribution functions of control and treatment outcomes, and  statistical inference methods for nonlinear maps usually rely on smoothness through a type of differentiability.
After revision: This paper develops a novel approach to uniform inference for the optimal value function, that is, the function that results from optimizing an objective function marginally over one of its arguments. The marginal optimization map is nonlinear and statistical inference methods for nonlinear maps usually rely on smoothness through a type of differentiability.