  Strong gravitational lensing provides a purely gravitational means to infer
properties of dark matter halos and thereby constrain the particle nature of
dark matter. Strong lenses sometimes appear as four lensed images of a
background quasar accompanied by spatially-resolved emission from the quasar
host galaxy encircling the main deflector (lensed arcs). We present methodology
to simultaneously reconstruct lensed arcs and relative image magnifications
(flux ratios) in the presence of full populations of subhalos and line-of-sight
halos. To this end, we develop a new approach for multi-plane ray tracing that
accelerates lens mass and source light reconstruction by factors of $\sim
100-1000$. Using simulated data, we show that simultaneous reconstruction of
lensed arcs and flux ratios isolates small-scale perturbations to flux ratios
by dark matter substructure from uncertainties associated with the main
deflector mass profile on larger angular scales. Relative to analyses that use
only image positions and flux ratios to constrain the lens model, incorporating
arcs strengthens likelihood ratios penalizing warm dark matter (WDM) with a
suppression scale $m_{\rm{hm}} / M_{\odot}$ in the range $\left[10^7 -
10^{7.5}\right]$, $\left[10^{7.5} - 10^{8}\right]$, $\left[10^8 -
10^{8.5}\right]$, $\left[10^{8.5} - 10^{9}\right]$ by factors of $1.3$, $2.5$,
$5.6$, and $13.1$, respectively, for a cold dark matter (CDM) ground truth. The
$95\%$ exclusion limit improves by 0.5 dex in $\log_{10} m_{\rm{hm}}$. The
enhanced sensitivity to low-mass halos enabled by these methods pushes the
observational frontier of substructure lensing to the threshold of galaxy
formation, enabling stringent tests of any theory that alters the properties of
dark matter halos.
