Smoothness of harmonic morphisms in full generality

Prove that every continuous harmonic morphism between measured sub-Riemannian manifolds is smooth, without assuming that the target is harmonically homogeneous or that the map preserves horizontal curves.

Background

The paper establishes smoothness under two separate sets of hypotheses: preservation of horizontal curves, and harmonic homogeneity of the target. It leaves unresolved whether smoothness holds for arbitrary harmonic morphisms between measured sub-Riemannian manifolds.