MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

Your "social reading platform" looks like what HTML and the WWW=World-Wide-Web was supposed to be when Tim Berners-Lee first set up a web-server and web-browser platform applications at CERN on a NeXT machine using Objective-C (I think he programmed it in objective C). Researchers were supposed to have their web pages listing and highligthing their research with hyperlinks pointing to the publications and datasets. If you look at the majority of academic webpages, the pulication and research interests are listed in that way. It's just that the majority of the internet world has gone into walled gardens such as the social media pages, with the cost of entry usually being the loss of any privacy or control over what can be done with your user-provided content. Look at the issues discussed on the meta website here at mathoverflow about why there hasn't been an upgrade to the StackExchange 2.0 software.

Wiki pages (not just that encyclopedic site that everyone uses, but a wiki page and wiki server which you can set up for yourself) allow for multiple users to modify a text using html or internal markup language. The requirement that $\LaTeX$ be usable in the markup language may require the use of MathML, or MathJax, or the jsMath package.

I think the correct answer is most likely an internal wiki server, with password-accessed accounts for modifying the wiki-pages. The problem is going to lie in placing a full copy of possibly copy-righted material, particularly in the case of wanting to do an "annotated version" of a research paper, or of a book chapter. If the author of a particular paper or book chapter, or the full book itself, wanted to do the experiment and set up their own wiki for the paper or book, and allow either free-for-all access or password-required gateway granted access to allow modifications and annotations, I would be very interested in taking part in that collaborative effort.