  On the basis of a number of Swampland conditions, we argue that the Hilbert
space of baby universe states must be one-dimensional in a consistent theory of
quantum gravity. This scenario may be interpreted as a type of "Gauss's law for
entropy" in quantum gravity, and provides a clean synthesis of the tension
between Euclidean wormholes and a standard interpretation of the holographic
dictionary, with no need for an ensemble. Our perspective relies crucially on
the recently-proposed potential for quantum-mechanical gauge redundancies
between states of the universe with different topologies. By an application of
the state-operator correspondence, this proposal rules out the possibility of
nontrivial, strictly well-defined bulk operators supported in a compact region.
We further comment on the possible exceptions in $d\leq 3$ for this hypothesis,
and the role of an ensemble for holographic theories in low dimensions, such as
JT gravity in $d = 2$ and possible cousins in $d=3$. We argue that these
examples are incomplete physical theories that should be viewed as branes in a
higher dimensional theory of quantum gravity, for which an ensemble plays no
role.
