  We present the study of the landscape structure of athermal soft spheres both
as a function of the packing fraction and of the energy. We find that, on
approaching the jamming transition, the number of different configurations
available to the system has a steep increase and that a hierarchical
organization of the landscape emerges. We use the knowledge of the structure of
the landscape to predict the values of thermodynamic observables on the edge of
the transition.
