Where do the roll odds come from?
The game prints them itself. Every roll shows a '1 in N' banner above the result, and objects already placed on a base carry the same label overhead, so a single endgame screenshot confirms a dozen at once.
Why do some objects have no rarity?
Because we have only ever seen them with a mutation applied. Mutations raise the displayed tier, so reading 'Divine' off a Galaxy version tells you nothing reliable about the plain one.
Do stats keep growing forever?
No. Objects stop at level 64, which is where the index shows '[MAX]'. The level calculator on each object page caps there.
Do stats climb evenly with level?
No. On the one object we could read at three different levels, the amount gained per level itself rises by a fixed 579.4 each time, so the total follows a curve. Objects with only one reading are projected in a straight line, which undershoots near the level cap.
Is this every object in the game?
Not yet. The in-game index counts 56 slots and we have 98 entries here, several of which are name-only. The gaps are marked rather than filled with guesses.