  We establish a sharp estimate for $k$-additive energies of subsets of the
discrete hypercube conjectured by de Dios Pont, Greenfeld, Ivanisvili, and
Madrid in arXiv:2112.09352, which generalizes a result by Kane and Tao. This
note proves the only missing ingredient, which is an elementary inequality for
real numbers, previously verified only for $k\leq100$. We also give an
interpretation of this inequality in terms of a lazy non-symmetric simple
random walk on the integer lattice.
