Is there a sharp boundary between airless and atmosphere-bearing planets?

Test whether atmosphere retention among rocky exoplanets follows the cosmic shoreline relation $I \text{ proportional to } v_{\mathrm{esc}}^4$ (I the cumulative XUV or bolometric instellation, v_esc the escape speed) proposed from Solar System bodies, and measure its location and width for M-dwarf and FGK hosts. The answer is the boundary in the $(v_{\mathrm{esc}}, I)$ plane with its scatter.

Atmosphere detections and non-detections for a sample of rocky planets spanning at least an order of magnitude in $v_{\mathrm{esc}}$ and instellation.