Soliton stability is due to topological constraints, rather than integrability of the field equations. Integration theory defines integrability and integrals of measurable functions on a measure space. The integrability of Hamiltonian vector fields is an open question. Thus, a static spacetime is a stationary spacetime satisfying this additional integrability condition. The Darboux integrability of continuous functions follows almost immediately from this theorem. This is a special case of the Frobenius integrability theorem. Measurability of "g" is ensured, but continuity (or even Riemann integrability) is not. Flatness of the connection corresponds locally to the Frobenius integrability of the horizontal spaces. To explain quantum integrability, it is helpful to consider the free particle setting. Many body localized systems exhibit a phenomenon known as emergent integrability. It is possible to find boundary conditions which preserve the integrability of the model. This explains the Arnold-Liouville integrability. Integrability preserving boundary conditions for this extension can be found as well. The integrability condition can be proven in various ways, one of which is sketched below.