Walkthrough

There's a note in C.W.'s workshop that describes the device you're looking for.

From the mayor's office, exit through the door at the top of the wall — take the elevator up one floor from the main office room. Head along the wall and across the swing gate to just before the mine shaft entrance at the end.

Turn left and head toward the waterfall. Follow the path as far back as you can and around to the right until you see a small canyon leading into the dome wall flanked by wooden fences.

Go through, and it will deposit you in a new area of the junkyard. A long walk down the only path available here will bring you to an out of place chunk of rock and a ramp. Hit the button to drop the ramp and create a shortcut to the rest of the junkyard. Now you can turn your attention to the Swap Machine.

Based on C.W.'s and Farley's notes that you've found, you should be able to piece together a basic understanding of how they work. The machines are built around a certain type of seed from the Tree. Now that you've watered the Tree, its seeds are active again. These machines take a sphere of one planet and swap them with a corresponding sphere on another planet. This is why so much in Obduction is round — all the cut-and-pasted buildings and locations, the dome and Hunrath itself and Farley's house and sidewalk, for example. These Swap Machines are a smaller version that you can control like a teleporter.

Pull the lever and hit the button, and you'll be transported to Kaptar.