  When are athermal soft sphere packings jammed ? Any experimentally relevant
definition must at the very least require a jammed packing to resist shear. We
demonstrate that widely used (numerical) protocols in which particles are
compressed together, can and do produce packings which are unstable to shear -
and that the probability of generating such packings reaches one near jamming.
We introduce a new protocol that, by allowing the system to explore different
box shapes as it equilibrates, generates truly jammed packings with strictly
positive shear moduli G. For these packings, the scaling of the average of G is
consistent with earlier results, while the probability distribution P(G)
exhibits novel and rich scaling
