I don't know if my thinking is correct, but I might have figured out a way of sorting in, (technically), O(N). The problem is memory usage, which depends on the highest value in the set. It also affects sorting speed slightly, but still in the range of n.

And because it's extremely stupid, I don't know if I wanna share the details (in the first post at least) due to shame, but I would like to ask - what if the bullshit I came up with actually works? What would it change? Would it be meaningful at all?