  We show that any graph that is generically globally rigid in $\mathbb{R}^d$
has a realization in $\mathbb{R}^d$ that is both generic and universally rigid.
This also implies that the graph also must have a realization in $\mathbb{R}^d$
that is both infinitesimally rigid and universally rigid; such a realization
serves as a certificate of generic global rigidity.
  Our approach involves an algorithm by Lov\'asz, Saks and Schrijver that, for
a sufficiently connected graph, constructs a general position orthogonal
representation of the vertices, and a result of Alfakih that shows how this
representation leads to a stress matrix and a universally rigid framework of
the graph.
