  Recent theoretical advances have led to the creation of a unified phase
diagram for the thermal glass and athermal jamming transitions. This diagram
makes clear that, while related, the mode-coupling---or dynamic---glass
transition is distinct from the jamming transition, occurring at a finite
temperature and significantly lower density than the jamming transition.
Nonetheless, we demonstrate a pre-jamming transition in athermal frictionless
spheres which occurs at the same density as the mode-coupling transition and is
marked by percolating clusters of locally rigid particles. At this density in
both the thermal and athermal systems, individual motions of an extensive
number of particles become constrained, such that only collective motion is
possible. This transition, which is well below jamming, exactly matches the
definition of collective behavior at the dynamical transition of glasses. Thus,
we reveal that the genesis of rigidity in both thermal and athermal systems is
governed by the same underlying topological transition in their shared
configuration space.
