  We obtain a transference bound for vertices of corner polyhedra that connects
two well-established areas of research: proximity and sparsity of solutions to
integer programs. In the knapsack scenario, it gives an exponential (in the
size of support of a solution) improvement on previously known proximity
estimates. In addition, for general integer linear programs we obtain a
resembling result that connects the minimum absolute nonzero entry of an
optimal solution with the size of its support.
