*SPOILERS* End Letter Decode

-The ringed Moon (likely comprised of the debris/dead people from the "experiment" on Earth)
-Space
-the pedo geezer sucked into space...nonetheless, he's dead :)
-Real sky
-Earth
-"Underground" (Patema's people) the actual normal people. Likely descendants of survivors who conducted the experiment/or weren't affected by it.
-"Above ground" (Eiji's disillusioned "Aiga" people) the actual upside-down people living in a dystopia.
-Artificial atmosphere
-Artificial "Starry sky" (Actually just the metal bottom base...likely explaining why it was uninhabited)

So basically, Patema's people are the descendents of the people who built the underground world for Eiji's people to live in. After a very long time, both sides mostly forgot their origins and even the fact that their roles are actually reversed. If you want proof of Patema's people being the right-side-up people, you simply have to look at how all the platforms are designed in the "forbidden" areas. Also the Moon clearly shows which direction is the original "up".