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!
But why risk anything if the survival of their species depends on staying more advanced? It would have delayed humanity if they had kept it a secret. It would have been impossible or at least much harder to find out what is going on and how to counter it. (Is it done for the story and the dramaturgy of it? Is them acting meaningfully sacrificed to make the story more entertaining for the viewer? )
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.
Human authorities discover the Trisolarans via the ETO before the Trisolarans announce themselves. I guess at that point in the story the general public isn’t aware but governments already are.