  Recently, Saad, Shenker and Stanford showed how to define the genus expansion
of Jackiw-Teitelboim quantum gravity in terms of a double-scaled Hermitian
matrix model. However, the model's non-perturbative sector has fatal
instabilities at low energy that they cured by procedures that render the
physics non-unique. This might not be a desirable property for a system that is
supposed to capture key features of quantum black holes. Presented here is a
model with identical perturbative physics at high energy that instead has a
stable and unambiguous non-perturbative completion of the physics at low
energy. An explicit examination of the full spectral density function shows how
this is achieved. The new model, which is based on complex matrix models, also
allows for the straightforward inclusion of spacetime features analogous to
Ramond-Ramond fluxes. Intriguingly, there is a deformation parameter that
connects this non-perturbative formulation of JT gravity to one which, at low
energy, has features of a super JT gravity.
