I'll be blunt and say that I do not understand one bit of what Zima's plan is. It seems like a lot of something... that adds up to a lot of nothing.
If the role PM thing is actually allowed and not stopped - and provides something conclusive - I'll change my vote. But for now...
Your plan sounded like some overly complex way to prove being a guard. And being that it doesn't seem like it'd do that (if I'm even understanding the theory behind it, which I might not, considering how mathematically-challenged I am)... well, this seems like as good a place as any to start.