(color online) Phase diagram of infinite-dimensional amorphous hard spheres. Pressure p-packing fraction φ phase diagram for hard spheres. The white region indicates the regime where the (meta) basin structure is present, either as a simple stable glass or as a marginal fractal glass. The left-most boundary of the glass region is the threshold line. The ‘J-line’ of jammed packings is found along , which always falls within the marginal phase. Although solving the mean-field out-of-equilibrium dynamics of hard spheres remains an open problem, an adiabatically slow compression should leave the equilibrium liquid line and eventually reach the J-line, while remaining within the white region. The green lines are two examples of an adiabatic following of a glass state. The figure is reproduced from [67].