  In this paper we reconcile several different approaches to Ricci flow through
singularities that have been proposed over the last few years by Kleiner-Lott,
Haslhofer-Naber and Bamler. Specifically, we prove that every noncollapsed
limit of Ricci flows, as provided by Bamler's precompactness theorem, as well
as every singular Ricci flow from Kleiner-Lott, is a weak solution in the sense
of Haslhofer-Naber. We also generalize all path-space estimates from
Haslhofer-Naber to the setting of noncollapsed Ricci limit flows. The key step
to establish these results is a new hitting estimate for Brownian motion. A
fundamental difficulty, in stark contrast to all prior hitting estimates in the
literature, is the lack of lower heat kernel bounds under Ricci flow. To
overcome this, we introduce a novel approach to hitting estimates that
compensates for the lack of lower heat kernel bounds by making use of the heat
kernel geometry of space-time.
