I'm picturing one AI making itself smarter until it seizes control of everything. Ergo, its program would be a map to the future. Presumably someone retains admin on it from when it was a baby.

Well, think about it. We are talking about a self-improving AI. It literally changes itself. You start with a seed AI, let's call it AI-0, and it bootstraps itself to an omnipotent AI which we can call AI-1.

Note that the programmers have no idea how to construct AI-1. They have no idea about the path from AI-0 to AI-1. All they (and we) know is that AI-0 and AI-1 will very very different.

Given this, I don't think that the program will be a map to the future. I don't think that the concept of "retaining admin" would even make sense for an AI-1. It will be completely different from what it started as. And I fail to see why you have a firm belief that it will be docile and obedient.