So the computer based solution proposed by Newton and Turing is rejected because the system is chaotic, meaning a general solution will always diverge from reality.
What I don't get is: this should still be good enough Run your solution every month or so, with updated measurements, and you'll have an ongoing "forecast" of conditions.
I'm referencing weather because that's we do. A weather forecast is a prediction of a chaotic system, but of one which changes every day or so. Prediction difficulty is dependent on local conditions and weather type, but we can still make predictions.
A gravitational system of 4 mutually interacting bodies is muuuuuch simpler than weather, and could be predicted far enough in advance to let a civilization adapt and persist!
The LORD does not care. Let the bugs play their little games and try to find a way out. The sophons will prevent them from doing anything that could actually prevent the invasion.
In fact, them panicking and putting all their hopes on false promises might make things easier in the long run.