  The nuclear charge radius of $^{32}$Si was determined using collinear laser
spectroscopy. The experimental result was confronted with ab initio nuclear
lattice effective field theory, valence-space in-medium similarity
renormalization group, and mean field calculations, highlighting important
achievements and challenges of modern many-body methods. The charge radius of
$^{32}$Si completes the radii of the mirror pair $^{32}$Ar - $^{32}$Si, whose
difference was correlated to the slope $L$ of the symmetry energy in the
nuclear equation of state. Our result suggests $L \leq 60$\,MeV, which agrees
with complementary observables.
