  Discrete derived categories were studied initially by Vossieck
\cite{Vossieck} and later by Bobi\'nski, Gei\ss, Skowro\'nski \cite{BGS}. In
this article, we define the CW complex of silting pairs for a triangulated
category and show that it is contractible in the case of discrete derived
categories. We provide an explicit embedding from the silting CW complex into
the stability manifold. By work of Qiu and Woolf, there is a deformation
retract of the stability manifold onto the silting pairs CW complex. We obtain
that the space of stability conditions of discrete derived categories is
contractible.
