  We construct a tensor network representation of the 3d toric code ground
state that is stable to a generating set of uniform local tensor perturbations,
including those that do not map to local operators on the physical Hilbert
space. The stability is established by mapping the phase diagram of the
perturbed tensor network to that of the 3d Ising gauge theory, which has a
non-zero finite temperature transition. More generally, we find that the
stability of a topological tensor network state is determined by the form of
its virtual symmetries and the topological excitations created by virtual
operators that break those symmetries. In particular, a dual representation of
the 3d toric code ground state, as well as representations of the X-cube and
cubic code ground states, for which point-like excitations are created by such
operators, are found to be unstable.
