because that you know genuinely depends on a lot of constants as we'll see but it does converge exponentially fast in this separation constant as the theorem 4 says with query psi after one update the distance of the new point to the fixed point is exponentially small in the separation delta i the precise bound using the jacobian and its value in the mean value theorem are the following so here you can see this is the distance between the updated psi after one step and the um and the fixed point right here this is what it converges to