Determining Model-independent $H_0$ and Consistency Tests
  We determine the Hubble constant $H_0$ precisely ($2.3\%$ uncertainty) in a
manner independent of cosmological model through Gaussian process regression,
using strong lensing and supernova data. Strong gravitational lensing of a
variable source can provide a time-delay distance $D_{\Delta t}$ and angular
diameter distance to the lens $D_{\rm{d}}$. These absolute distances can anchor
Type Ia supernovae, which give an excellent constraint on the shape of the
distance-redshift relation. Updating our previous results to use the H0LiCOW
program's milestone dataset consisting of six lenses, four of which have both
$D_{\Delta t}$ and $D_{\rm{d}}$ measurements, we obtain
$H_0=72.8_{-1.7}^{+1.6}\rm{\ km/s/Mpc}$ for a flat universe and
$H_0=77.3_{-3.0}^{+2.2}\rm{\ km/s/Mpc}$ for a non-flat universe. We carry out
several consistency checks on the data and find no statistically significant
tensions, though a noticeable redshift dependence persists in a particular
systematic manner that we investigate. Speculating on the possibility that this
trend of derived Hubble constant with lens distance is physical, we show how
this can arise through modified gravity light propagation, which would also
impact the weak lensing $\sigma_8$ tension.
