Approaching space time trough velocity in Doubly Special Relativity

We discuss the definition of velocity as dE/d|p|, where E,p are the energy and momentum of a particle, in Doubly Special Relativity (DSR). If this definition matches dx/dt appropriate for the space-time sector, then space-time can in principle be built consistently with the existence of an invariant length scale. We show that, within different possible definitions, this program fails, and this is a strong indication that the DSR spacetime sector cannot be considered a continuous differentiable manifold.