Wow, two pages of replies since last time I checked.
So just a quick lore check people: In the Three Fairies manga, there was a tree behind Reimu's Shrine, that got hit by lightning, split into two. Reimu thought it as a good sign and she did venerate the tree for a day, but then forgotten about it. As it turned out, the tree lie at the exact middle of the border between Gensokyo and the Outside World. When the lighting hit it, it caused a large hole to rip open in the border. However, the tree's Outside World version quickly replaced the old tree, and then Yukari allowed the Three Fairies to move into the new tree, because fairies are basically the natural energy of Gensokyo itself, so with them living there on the border, their presence would sooner or later mend the hole in the border.
Since Purvis' Quests do follow the canon lore quite a bit, I think it's safe to say that the Old Tree was the Branch Entity. And the memories might mean that you should check out the three fairies' tree behind Reimu's shrine.