This is kind of an interesting idea: it's a proposal for a new way to show message threads that differs from the standard way in that, instead of the "message pane" showing just a single message, it shows all the messages in the thread, more like an indented web forum.
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The other interesting part is that the tree structure is somewhat interleaved: normally, message threads are arranged by making a tree of parent/child relationships, and then sorting siblings by date. This gives a lot of priority to tree structure and very little priority to date: when new messages are added, they might show up anywhere in the tree, depending on which message they are a reply to. This is a slight misfeature of every threading system I've used, including the ones I wrote: you often have to turn off threading to be able to find things.
The proposed model uses the X axis for "replies" and the Y axis for "time". So you still get indentation showing who replied to who; but you can also assume that the newest posts are at the bottom. That's a pretty good trick!
One disturbing thing about their presentation is that making it be usable requires the software to throw away a lot of message content: they seem to be assuming that for this to look good, it'd have to recognise and strip out redundant quoted text in the messages. That's somewhat scary.
I found it very frustrating to read that PDF, because it's been a long time since I've read something that was structured as a "research paper", and I find that footnotes just drive me crazy! I want links, not footnotes. Even worse that, when you finally get to the footnotes page at the end, there are no links there either: there are titles and page numbers. You know, dead trees! What century is this?