  We consider a finite-dimensional oscillatory integral which provides a
"finite-dimensional model" for analytically continued $SU(2)$ Chern-Simons
theory on closed 3-manifolds that are described by plumbing trees. This model
allows an efficient description of Stokes phenomenon for perturbative
expansions in Chern-Simons theory around classical solutions -
$SL(2,\mathbb{C})$ flat connections. Moreover, the Stokes coefficients can be
categorified, i.e. promoted to graded vector spaces, in terms of this
finite-dimensional model. At least naively, the categorification gives BPS
spectrum of 5d maximally supersymmetric Yang-Mills theory on the 3-manifold
times a line with appropriate boundary conditions. We also comment on necessity
of taking into account "flat connections at infinity" to capture Stokes
phenomenon for certain 3-manifolds.
