I will say this. "The District" performance of the game is the most comparable to the beta, of any game that I have ever played. For me it was smooth in beta as it is in game. I haven't even looked what the official specs are...
I know you know, you will have to keep it on low settings, and that your machine is screaming for another 8 gig of RAM to be a lot happier and to extend it's life.