Semi-classical Szegő kernel asymptotics on CR manifolds of high codimension

In this paper, we consider a CR manifold $X$ of high codimension and a CR line bundle $L$ over $X$. For each $k \in \mathbb{N}$, let $L^k$ denote the $k$-th power of $L$. We establish that the spectral projection $Π_{k,\leq kμ_k} := \mathbf{1}_{(-\infty, kμ_k]}(\Box_{b,k})$ converges to the weighted