AdS$_3$ Pure Gravity and Stringy Unitarity

We construct a unitary, modular-invariant torus partition function of a two-dimensional conformal field theory with a Virasoro primary spectral gap of $\Delta_* = \frac{c-1}{12}$ above the vacuum. The twist gap is identical, apart from two states $\mathcal{O}_*$ with spin scaling linearly in the central charge $c$. These states admit an AdS$_3$ interpretation as strongly coupled strings. All other states are black hole microstates.