  Let $(X,g)$ be a compact manifold with conic singularities. Taking $\Delta_g$
to be the Friedrichs extension of the Laplace-Beltrami operator, we examine the
singularities of the trace of the half-wave group $e^{- i t \sqrt{
\smash[b]{\Delta_g}}}$ arising from strictly diffractive closed geodesics.
Under a generic nonconjugacy assumption, we compute the principal amplitude of
these singularities in terms of invariants associated to the geodesic and data
from the cone point. This generalizes the classical theorem of
Duistermaat-Guillemin on smooth manifolds and a theorem of Hillairet on flat
surfaces with cone points.
