Finiteness of leaps of modules of integrable derivations of algebras of finite type

We prove the finiteness of leaps of modules of $m$-integrable derivations for algebras essentially of finite type and, more generally, for schemes essentially of finite type over an algebraically closed field of positive characteristic. This provides an affirmative answer to a question posed by L. Narváez Macarro. As an application, we establish the coherence of the module of $\mathrm{\infty }$-integrable derivations.