The whole idea of falsifiability, i.e. testing, has already been discussed at length in this thread.
I wasn't talking about "testing" in that sense.
I meant make a mathematical model of his behaviour and effect upon the world.
Next, where does an authoritative definition of scientific theory or hypothesis states that a scientific theory or hypothesis must predict future behavior of things?
That's what science does - it provides (mathematical) models of how how things behave: i.e. if this theory is correct then things will behave in such and such a fashion.
That's why science relies so heavily on mathematics - reduce it to an amenable mathematical model (gravity, ballistics, heat transfer - they are all predictions of behaviour, for example, if I let go of a ball from a height of 2 metres I can make predictions on when it will reach the ground, and at what speed).
How can "god" fit into this system?
Simple, he can't, it is impossible to determine at all what "god" will do, or what effect he will have under any set of circumstances, since he is, by definition, supernatural and can make up his own rules at whim.
Okay, I know it's Wiki, but:
The underlying goal or purpose of science to society and individuals is to produce useful models of reality. To achieve this, one can form hypotheses based on observations that they make in the world. By analyzing a number of related hypotheses, scientists can form general theories. These theories benefit society or human individuals who make use of them.
In short, science produces models with useful predictions.
What possible hypotheses can you form from "god"?
What possible model of reality can you get from him?