Ball Lock Puzzle

Here's an amusing little puzzle I'm sure you never saw before because I just invented it. I've been calling it the z=xy puzzle; read on to find out why. It is a more complex version of my 2 piece cube puzzle, but now including a magic ball lock. It is part puzzle, part magic trick, part math lesson. The theory that makes it work comes from pure mathematics. Once the cube is closed and locked by rotating the ball, the cube is held closed by invisible mathematical forces. Normally, a sphere would not be retained in a hemispherical cavity, but not in this case. What gives?
You start with the cube in two halves, each side holding half of a ball. Show your victim, I mean the audience, the inside of the cube and point out how the inside surfaces are all smooth with no overhangs to hold the cube together. Slide the cube halves all the way together to form a solid cube and then apart again to demonstrate that the cube opens and closes freely. Now close the cube and hand it to an audience memb