  Thurston's sphere packing on a 3-dimensional manifold is a generalization of
Thusrton's circle packing on a surface, the rigidity of which has been open for
many years. In this paper, we prove that Thurston's Euclidean sphere packing is
locally determined by combinatorial scalar curvature up to scaling, which
generalizes Cooper-Rivin-Glickenstein's local rigidity for tangential sphere
packing on 3-dimensional manifolds. We also prove the infinitesimal rigidity
that Thurston's Euclidean sphere packing can not be deformed (except by
scaling) while keeping the combinatorial Ricci curvature fixed.
