  One of the leading mechanisms invoked to explain the existence of the radius
valley is atmospheric mass loss driven by X-ray and extreme-ultraviolet
irradiation, with this process stripping the primordial envelopes of young,
small planets to produce the observed bimodal distribution. We present an
investigation into the TOI-431 and $\nu^2$ Lupi planetary systems, both of
which host planets either side of the radius valley, to determine if their
architectures are consistent with evolution by the XUV mechanism. With
$\textit{XMM-Newton}$, we measure the current X-ray flux of each star, and see
evidence for a stellar flare in the TOI-431 observations. We then simulate the
evolution of all of the transiting planets across the two systems in response
to the high-energy irradiation over their lifetimes. We use the measured X-ray
fluxes as an anchor point for the XUV time evolution in our simulations, and
employ several different models of estimating mass loss rates. While the
simulations for TOI-431b encountered a problem with the initial calculated
radii, we estimate a likely short ($\sim$ Myr) timespan for primordial envelope
removal using reasonable assumptions for the initial planet. $\nu^2$ Lupi b is
likely harder to strip, but is achieved in a moderate fraction of our
simulations. None of our simulations stripped any of the lower density planets
of their envelope, in line with prediction. We conclude that both systems are
consistent with expectations for generation of the radius valley through XUV
photoevaporation.
