In other words: for many disciplines, the potential replacements providing peer review, archival and distribution are already there. The main thing a replacement system will have to find out is how to determine who to give grants, tenure, etc.
(Disclaimer: I'm working on a project that hopes to achieve that.)
It's not currently that interesting to the average HN reader though. The idea is to allow researchers to give each other recognition explicitly, ideally replacing the recognition of "being published in journal x". Since researchers already have a reputation in their academic community, we figured that we could leverage that as a counterweight to the indirect reputation that journals currently have.
We do so by integrating with preprint servers and publishers, providing a widget that allows researchers to endorse the research they're reading. The first integrations are set to launch at the start of 2019, so until then there's not much to play with.
That said, the PageRank-like system you might be looking for could just be the h-index? https://en.wikipedia.org/wiki/H-index