  We search for evidence of the cause of the exoplanet radius gap, i.e. the
dearth of planets with radii near $1.8\ R_\oplus$. If the cause was
photoevaporation, the radius gap should trend with proxies for the early-life
high-energy emission of planet-hosting stars. If, alternatively, the cause was
core-powered mass loss, no such trends should exist. Critically, spurious
trends between the radius gap and stellar properties arise from an underlying
correlation with instellation. After accounting for this underlying
correlation, we find no trends remain between the radius gap and stellar mass
or present-day stellar activity as measured by near-UV emission. We dismiss the
nondetection of a radius gap trend with near-UV emission because present-day
near-UV emission is unlikely to trace early-life high-energy emission, but we
provide a catalog of GALEX near-UV and far-UV emission measurements for general
use. We interpret the nondetection of a radius gap trend with stellar mass by
simulating photoevaporation with mass-dependent evolution of stellar
high-energy emission. The simulation produces an undetectable trend between the
radius gap and stellar mass under realistic sources of error. We conclude that
no evidence, from this analysis or others in the literature, currently exists
that clearly favors either photoevaporation or core powered mass loss as the
primary cause of the exoplanet radius gap. However, repeating this analysis
once the body of well-characterized $< 4\ R_\oplus$ planets has roughly doubled
could confirm or rule out photoevaporation.
