The semiclassical limit of unit-area quantum disks

Fix $W\in(0,2)$ and let $γ\downarrow0$. We prove that a weight-$W$ quantum disk conditioned to have unit quantum area converges, in the maximum-embedded strip, to the deterministic field $ϕ_W(t+iθ)=\log(W/(4π))-2\log\cosh(Wt/2)$ and its constant-curvature area measure. The proof establishes a joint