  For the first time, a gravitational calculation was recently shown to yield
the Page curve for the entropy of Hawking radiation, consistent with unitary
evolution. However, the calculation takes as essential input Hawking's result
that the radiation entropy becomes large at late times. We call this apparent
contradiction the state paradox. We exhibit its manifestations in standard and
doubly-holographic settings, with and without an external bath. We clarify
which version(s) of the Ryu-Takayanagi prescription apply in each setting. We
show that the two possible homology rules in the presence of a braneworld
generate a bulk dual of the state paradox. The paradox is resolved if the
gravitational path integral computes averaged quantities in a suitable ensemble
of unitary theories, a possibility supported independently by several recent
developments.
