Episode 63: Pages 239-253 of volume 4 of the Kodansha publication. [source]
In this chapter, Kei finds out Miyako went into a coma during experimentation, and her records were removed from all testing which allowed her to exist beyond the lab. Meanwhile, Colonel's scientist is not as trustworthy as previously thought, the Great Tokyo Empire is mobilizing towards Miyako's temple, and Tetsuo says he has quit taking drugs cold turkey.
I haven't noticed until now just how long it's been since Kaneda was in the story. I guess I was just waiting for his time to turn up again, but he still hasn't. It makes a little more sense now why the fourth and fifth volumes are named after Kei, but so far it seems more like Miyako and Tetsuo have been the main driving forces of the plot. Now I wonder what's going on with Kaneda.
Also @almightybismarck what you're describing happened in chapter 60. The true halfway point of the story. That was quite a hefty chunk of lore to take in.