With all pieces of the 4D chess in movement, it's hard to predict exactly what Kyle, Rishe, Arnold and Sensei are going to do. But I have a good guess on how the plot will connect Rishe tracking Sensei with the alliance:
Probably spoilers
Black powder + careful machining on metallic parts = firearms. They have immediate warfare application, and should be enough to convince Arnold that an alliance with Coyolles is desirable.
If that's what's going to happen or not, we'll only know it next week.
I think the potential for guns is exactly why Rishe doesn't want Arnold to meet the professor about it though. Galkhein is already very destructive without it. Imagine them with guns and explosives.