Super-Brownian motion is one of the most important stochastic PDE and measure-valued processes, with a strong motivation from population biology. However, uniqueness for the equation describing this process is still unknown. Since the coefficients are at their worst when the solution is close to 0, studying the boundary of the support of the solution seems like a reasonable strategy for establishing uniqueness. We compute the Hausdorff dimension of the boundary of the support, but we do not yet have a proof of uniqueness.