the spike so the equations are not are not exactly the same so this you know this is something that is quite probably not so complicated to to generalize these proofs including this the spine but it hasn't been done yet so i will not be talking about that instead i will be talking about what happens if we solve these equations what insight can we get about the behavior of this optimization problem so this is depicted here so as a function of the iteration time i am plotting the correlation with the ground roof