It's a tree laid out more-or-less intuitively (like a mind map) on a two dimensional plane which someone is calling a map (you can quibble with the term "map" if you like but it's not a mind-bendingly incomprehensible term) in this context. It's not a power set, there would appear to be multiple singly rooted n-ary trees. You start with an initial query (the root node) and the generated ChatGPT responses (they are called cards here) branch out like a tree rather than being a linear back-and-forth convo – structured like, as I said, a mind map https://en.wikipedia.org/wiki/Mind_map
It seems you’re making a https://en.m.wikipedia.org/wiki/Hierarchy_(mathematics) which isn’t dimensional in any nature. It’s like saying that hacker news is a “2d forum”…
Anyway ordering it more like https://en.m.wikipedia.org/wiki/Power_set
Just seems natural to me. Information typically isn’t hierarchal outside of artificial structures.