Did Mirai Kuriyama really rebuild her body, or what really happened to it? Mirai's body vanished/consumed/disintegrated during the battle vs Kyoukai no Kanata, then there is this version of her in Akihito's "dream world" that dissolves on-screen, then months(?) later she is alive in flesh and blood (pun intended).

So, what happened?  Was her blood control so high that she willed herself back into a physical body, or is it some Applied Phlebotinum fiat?
I know this is sort of a zombie, sorry, and purely speculation on my part, but I think it went like so:

Mirai initially vanished by absorbing KnK into her body, so she was intermingled with it from the beginning... but she was never really dead.

With KnK exerting all its power to combat her blood, another dimension is created, but their existence in that world is a supernatural manifestation of virtually incorporeal beings.  KnK has to use all focus fighting her blood which is a constant assailant on its very core, and somehow this is created.  Though the exact reason this phenomenon occurs and the function thereof is not crystal clear, it's fairly tertiary to this point, so I'll avoid the digression.

After the battle, KnK's not as strong as it once was, since it took a pretty bad pounding.  Weakened (despite outside interference, to said party's astonishment), Aki is able to subdue KnK entirely having learned to control a mere fraction of KnK's full power, and he absorbs it back into his body (which actually includes Mirai as well).  Since it's Aki's force of will now actively taking control of it, rather than just fighting in the same vessel, Mirai vanishes because as KnK is no longer the one willing the alternate dimension where she'd manifest into existence.  She's really still inside KnK, which Aki absorbed and has at least partial control of.

Later, his extreme desire to see her again, and to relive his memories of the first meeting, are so potent that he actually exercises some of KnK's power subconsciously, extracting her from it and placing her right where he most wanted her to be.  He knew what he was thinking at the time, and rushed to the place he had seen her in his mind, knowing that the ring vanishing meant she had been reunited with it, as was his most profound desire.

Could be wrong though.  Take it or leave it :)