  At a fixed halo mass, galaxy clusters with higher magnitude gaps have larger
brightest central galaxy (BCG) stellar masses. Recent studies have shown that
by including the magnitude gap ($\rm m_{gap}$) as a latent parameter in the
stellar mass - halo mass (SMHM) relation, we can make more precise measurements
on the amplitude, slope, and intrinsic scatter. Using galaxy clusters from the
Sloan Digital Sky Survey, we measure the SMHM-$\rm m_{gap}$ relation and its
evolution out to $z=0.3$. Using a fixed comoving aperture of 100kpc to define
the central galaxy's stellar mass, we report statistically significant negative
evolution in the slope of the SMHM relation to $z = 0.3$ ($> 3.5\sigma$). The
steepening of the slope over the last 3.5 Gyrs can be explained by late-time
merger activity at the cores of galaxy clusters. We also find that the inferred
slope depends on the aperture used to define the radial extent of the central
galaxy. At small radii (20kpc), the slope of the SMHM relation is shallow,
indicating that the core of the central galaxy is less related to the growth of
the underlying host halo. By including all of the central galaxy's light within
100kpc, the slope reaches an asymptote at a value consistent with recent high
resolution hydrodynamical cosmology simulations.
