How compression modifies the free modes
Compression adds contacts-per-particle z above the isostatic number 6 (in 3D)
Each new contact blocks one of the L2 free modes
Number of added contacts ~ (z - 6) L3
When (z - 6) L3 > (constant) L2,   free modes are all blocked
...modes of size > L are like an ordinary solid
Still, small subregions of size L* < (constant) /(z-6) are ~unperturbed
Simulation confirms prediction:
excess contacts
1
w* µ
excess contacts
per particle
Thus the density D(w) is ~ unperturbed for w > w* ~ 1/L* ~ (z-6)