  There is exactly one bosonic (3+1)-dimensional topological order whose only
nontrivial particle is an emergent boson: pure $\mathbb{Z}_2$ gauge theory.
There are exactly two (3+1)-dimensional topological orders whose only
nontrivial particle is an emergent fermion: pure "spin-$\mathbb{Z}_2$" gauge
theory, in which the dynamical field is a spin structure; and an anomalous
version thereof. I give three proofs of this classification, varying from
hands-on to abstract. Along the way, I provide a detailed study of the braided
fusion $2$-category $\mathcal{Z}_{(1)}(\Sigma \mathbf{SVec})$ of string and
particle operators in pure spin-$\mathbb{Z}_2$ gauge theory.
