  We study the quantum error correction properties of the black hole interior
in a toy model for an evaporating black hole: Jackiw-Teitelboim gravity
entangled with a non-gravitational bath. After the Page time, the black hole
interior degrees of freedom in this system are encoded in the bath Hilbert
space. We use the gravitational path integral to show that the interior density
matrix is correctable against the action of quantum operations on the bath
which (i) do not have prior access to details of the black hole microstates,
and (ii) do not have a large, negative coherent information with respect to the
maximally mixed state on the bath, with the lower bound controlled by the black
hole entropy and code subspace dimension. Thus, the encoding of the black hole
interior in the radiation is robust against generic, low-rank quantum
operations. For erasure errors, gravity comes within an $O(1)$ distance of
saturating the Singleton bound on the tolerance of error correcting codes. For
typical errors in the bath to corrupt the interior, they must have a rank that
is a large multiple of the bath Hilbert space dimension, with the precise
coefficient set by the black hole entropy and code subspace dimension.
