Fig. 4.

Numerical density of states $D\left(\omega \right)$ for a hard-sphere glass in $d=2$, at pressure $p={10}^{12}$, in (Left) log–log axes and (Right) linear axes. The triangle has the predicted slope $-0.17$, assuming ${\theta }_e=0.41$, as discussed in the main text. The characteristic frequency ${\omega }^{\mathrm{\ast }}$ is expected to be $\sim {10}^{-6}{\omega }_c$, outside the accessible numerical range at this pressure.