  We study the spectral form factor (SFF) of general topological gravity in the
limit of large time and fixed temperature. It has been observed recently that
in this limit, called the tau-scaling limit, the genus expansion of the SFF can
be summed up and the late-time behavior of the SFF such as the ramp-plateau
transition can be studied analytically. In this paper we develop a technique
for the systematic computation of the higher order corrections to the SFF in
the strict tau-scaling limit. We obtain the first five corrections in a closed
form for the general background of topological gravity. As concrete examples,
we present the results for the Airy case and Jackiw-Teitelboim gravity. We find
that the above higher order corrections are the Fourier transforms of the
corrections to the sine-kernel approximation of the Christoffel-Darboux kernel
in the dual double-scaled matrix integral, which naturally explains their
structure. Along the way we also develop a technique for the systematic
computation of the corrections to the sine-kernel formula, which have not been
fully explored in the literature before.
