  The duality of Jackiw-Teitelboim (JT) gravity and a double scaled matrix
integral has led to studies of the canonical spectral form factor (SFF) in the
so called $\tau-$scaled limit of large times, $t \to \infty$, and fixed
temperature in order to demonstrate agreement with universal random matrix
theory (RMT). Though this has been established for the unitary case, extensions
to other symmetry classes requires the inclusion of unorientable manifolds in
the sum over geometries, necessary to address time reversal invariance, and
regularization of the corresponding prime geometrical objects, the
Weil-Petersson (WP) volumes. We report here how universal signatures of quantum
chaos, witnessed by the fidelity to the Gaussian orthogonal ensemble, emerge
for the low-energy limit of unorientable JT gravity, i.e. the Airy
model/topological gravity. To this end, we implement the loop equations for the
corresponding dual (double-scaled) matrix model and find the generic form of
the Airy WP volumes, supported by calculations using unorientable Kontsevich
graphs. In an apparent violation of the gravity/chaos duality, the
$\tau-$scaled SFF on the gravity side acquires both logarithmic and power law
contributions in $t$, not manifestly present on the RMT side. We show the
expressions can be made to agree by means of bootstrapping-like relations
hidden in the asymptotic expansions of generalized hypergeometric functions.
Thus, we are able to establish strong evidence of the quantum chaotic nature of
unorientable topological gravity.
