  Recent observations on type III algebras in AdS/CFT raise the possibility
that smoothness of the black hole horizon is an emergent feature of the
large-$N$ limit. In this paper, we present a $bulk$ model for the finite-$N$
mechanism underlying this transition. We quantize a free scalar field on a BTZ
black hole with a Planckian stretched horizon placed as a Dirichlet boundary
for the field. This is a tractable model for the stretched horizon that does
not ignore the angular directions, and it defines a black hole vacuum which has
similarities to (but is distinct from) the Boulware state. Using analytic
approximations for the normal modes, we first improve upon 't Hooft's brick
wall calculation: we are able to match $both$ the entropy and the temperature,
$exactly$. Emboldened by this, we compute the boundary Wightman function of the
scalar field in a typical pure state built on our stretched horizon vacuum, at
an energy sliver at the mass of the black hole. A key result is that despite
the manifest lack of smoothness, this single-sided pure state calculation
yields precisely the Hartle-Hawking thermal correlator associated to the smooth
horizon, in the small-$G_N$ limit. At finite $G_N$, there are variance
corrections that are suppressed as $\mathcal{O}(e^{-S_{BH}/2})$. They become
important at late times and resolve Maldacena's information paradox. Highly
excited typical pure states on the stretched horizon vacuum are therefore
models for black hole microstates, while the smooth horizon describes the
thermal state. We note that heavy excited states on the stretched horizon are
better defined than the vacuum itself. These results suggest that
complementarity in the bulk EFT could arise from a UV complete bulk description
in which the black hole interior is not manifest.
