Yes, and as I said, the number of puzzle states is the number of nodes in the pictured graph, cubed. There is some relation between the two graphs, but they aren’t the same, and the pictured graph doesn’t necessarily show too clearly how to navigate around between different regions of the graph of game states.

Yes. That’s right. In problem analysis the problem state graph is implicit (or virtual, I’m not sure which is the appropriate term). It happen Ms that this puzzle also has a graph, but (agreeing with you) that’s not the psg. We could call the puzzle’s graph the “map” to be a bit less confusing, assuming we want to bother continuing this thread, but I’m guessing that it’s just you and me at this point, and we agree, so we should stop.