# Integrability and the Chaos-Proof Algorithm

We study the integrability problem of a non-perturbative quantum field theory on a unit sphere. We illustrate the problem with the identity of a set of points representing the main integrable points. We find that the integration of the points can be controlled by the fundamental interaction of the field theory. In addition to the step function, we study the integrability of the Jacobian of the points. We find that the Jacobian of the points is a product of two integrable functions. We also find that the two functions are integrable in the sense that they are integrable in terms of the physical variables of the points. We discuss the connection between the integration of the steps and the integrable functions. We find that the Jacobian of the steps is a product of two functions.