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The Toeplitz operator $\\Pi_\\tau D_{\\sqrt{\\rho}} \\Pi_\\tau$ associated to the Reeb vector field is a positive, self-adjoint, elliptic operator on $H^2(\\partial M_\\tau)$. We compute $\\lambda \\to \\infty$ asymptotics under parabolic rescaling in a neighborhood of the geodesic (Reeb) flow $G^{t}_{\\tau} = \\exp t\\Xi_{\\sqrt{\\rho}}$ for the spectral projection kernel $\\Pi_{\\chi, \\lambda}$ associated to $\\Pi_\\tau D_{\\sqrt{\\rho}} \\Pi_\\tau$. 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