This only works if: 1) your state is a linear function of time 2) you know the initial conditions 3) the time integral calculation of the state evolution ove

This only works if: 1) your state is a linear function of time 2) you know the initial conditions 3) the time integral calculation of the state evolution over time is trivial to do (e.g. constant velocity means distance travelled is simply time * velocity) It's not that you "don't need state", it's that your state calculation is entirely dependent on time T and initial conditions I, and it's calculable in ~roughly~ the same amount of time as an actual state update would take.