The pressure of the gluon plasma at $\mathcal{O}(g_s^6)$, perturbatively

We determine the four-loop hard-scale matching correction to the pressure of the gluon plasma at high temperature. This result completes the long-standing calculation through $\mathcal{O}(g_s^6)$, where $g_s$ is the strong coupling. Our result agrees, within uncertainties, with the value obtained in arXiv:1204.6184 by fitting the perturbative series to continuum-extrapolated lattice data, thereby providing the first direct test of the weak-coupling expansion at this order.