  We report a new analysis of the Hubble Frontier Fields clusters Abell 2744
and MACS 0416 using wavelet decomposition to remove the cluster light, enabling
the detection of highly magnified (>50x) galaxies a factor of 10x fainter in
luminosity than previous studies. We find 167 galaxies at z > 6, and with this
sample we are able to characterize the UV luminosity function to M_UV = -12.5
at z ~ 6, -14 at z ~ 7 and -15 at z ~ 8. We find a steep faint-end slope (alpha
<-2), and with our improved statistics at the faint end we reduce the
fractional uncertainty on alpha to <2% at z ~ 6 - 7 and 4% at z ~ 8. We also
investigate the systematic uncertainty due to the lens modelling by using every
available lens model individually and comparing the results; this systematic
fractional uncertainty on alpha is <4% at all redshifts. We now directly
observe galaxies in the luminosity regime where simulations predict a change in
the faint-end slope of the luminosity function, yet our results provide
statistically very strong evidence against any turnover in the luminosity range
probed, more consistent with simulations in which stars form in lower-mass
halos. Thus we find strong support for the extension of the steep luminosity
function to M_UV = -13 at z > 6, consistent with the number of faint galaxies
needed to reionize the Universe under standard assumptions.
