I think it's pretty likely this has little to do with Sony's E3 conference, but the small Italian studio Ovosonico that made Murasaki Baby for the Vita has been teasing their new PS4 game (not confirmed exclusive) on twitter the last month or so. They have every other day or so been tweeting out a total of
21 puzzle pieces. If you lay out the puzzle (see below), it becomes obvious that there's 7 pieces left. At the current pace of their tweets, that would mean that the puzzle will become complete close to the start of E3. Now I don't know if it's very common for smaller titles to be announced so close to the big shows but my first thought was that it could either be a VR game or one of those "releasing right now" games announced at one of the conferences. Thoughts?