less pessimistic limit than simply taking the $2\sigma$ upper mass limit at the $2\sigma$ magnitude limit, which is very conservative.

We present the black hole–stellar mass relation from the stellar mass limits of our $z\simeq6$ quasar hosts in Figure \[fig:BHmassRelation\]. Our limits are consistent with the black hole–stellar mass relation from existing sub-mm observations of $z\simeq6$ quasars, [@Willott2017; @Izumi2018; @Izumi2019; @Pensabene2020], which measure the dynamical mass of the host using gas dynamics as probed by the \[CII\] line, and assume $M_\ast=M_{\textrm{dyn}}$. Three of our quasars have dynamical mass measurements [@Wang2010; @Pensabene2020], which we also show in Figure \[fig:BHmassRelation\]. Our stellar mass upper limit for SDSS J2054-0005 lies above the measured dynamical mass of $M_{\textrm{dyn}}=0.7\substack{+4.5 \\ -0.3}\times10^{10}M_\odot$ [@Pensabene2020], suggesting that either our limit is significantly larger than the true stellar mass, with much deeper observations required to detect the underlying stellar emission, or the measured dynamical mass underestimates the total mass of the galaxy. Our stellar mass upper limit for SDSS J0129-0035 is consistent with the lower dynamical mass limit of $M_{\textrm{dyn}}>7.8\times10^{10}M_\odot$ [@Pensabene2020]. The lower limit on the dynamical mass for NDWFS J1425+3254 of $M_{\textrm{dyn}}>1.56\times10^{11}M_\odot$ [@Wang2010] is larger than our stellar mass upper limit, suggesting that we are close to detecting 