Let $n\ge 2$, let $\Omega\subset\mathbb C^n$ be a bounded domain with $C^\infty$ strictly pseudoconvex boundary $M:=\partial\Omega$, and let $d\mu$ be a positive $C^\infty$ density on $M$. Let $T^{1,0}M\subset \mathbb C TM$ and $T^{0,1}M\subset \mathbb C TM$ be the induced CR bundles, and let $H(M):=\operatorname{Re}(T^{1,0}M\oplus T^{0,1}M)\subset TM$ be the real contact distribution. Let
be the orthogonal Szegő projection. Denote by $S(x,y)$ the distribution kernel of $S$ with respect to the density $d\mu$ in the second variable.
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Let $\theta\in\Omega^1(M)$ be a positive contact form for the strictly pseudoconvex CR structure, meaning $\ker\theta=H(M)$ and the sign of $\theta$ agrees with the positive Levi orientation. Define the positive contact cone