The Liouvillianity conjecture for abelian relations of webs

Let $\mathcal W$ be a web, and let its abelian relations mean the relations among the defining foliations obtained by summing closed one-forms along the leaves. A Liouvillian extension of the field of definition of $\mathcal W$ is a differential-field extension obtained through successive adjunctions of solutions of linear differential equations, algebraic extensions, exponentials, and primitives. Liouvillianity conjecture. The abelian relations of $\mathcal W$ are Liouvillian. The paper notes that this holds for webs admitting infinitesimal automorphisms, where the abelian relations lie in a Liouvillian extension of the field of definition; the conjecture extends this assertion to arbitrary webs.