Homogeneous Universal H-fields

We consider derivations $\partial$ on Conway's field $\mathbf{No}$ of surreal numbers such that the ordered differential field $(\mathbf{No},\partial)$ has constant field $\mathbb{R}$ and is a model of the model companion of the theory of $H$-fields with small derivation. We show that this determines $(\mathbf{No},\partial)$ uniquely up to isomorphism, and that this structure is absolutely homogeneous universal for models of this theory with constant field $\mathbb{R}$.