There are 8 control points in the map but in human logic there are only 4 territories. The 4 middle control points are just there to say : 'this team currently has the advantage for this round'.
You don't need to know this to understand how to play the map, but the middle control points can also change allegiance while they're not in play, to avoid creating invalid rounds. For example, if the first round played is AB and BLU threatens B by capping AB-mid, the cp BC-mid will turn BLU (so that if BLU caps B and wins the round AB, you don't get to play a round BC where B and C are blu and the BC-mid is neutral). If RED then captures AB-mid and threatens A, BC-mid will return to neutral and AD-mid will turn red.
To put it simply : at the end of a round, if you own two adjacent corners (territories), you automatically own the cp between them, regardless of everything else. And if two adjacent corners are owned by different teams, the cp between them will automatically be neutral.
I got into a lot of invalid rounds and the game randomly locking up on a round victory (because it couldn't find out how many rounds were left to play) before I figured out how to get this to work.
And yet, there's still a small problem...