The model-completeness conjecture for the differential field of transseries

Let $\mathbb{T}$ be the ordered valued differential field of transseries. Let $H$-fields be ordered differential fields equipped with the associated $H$-field structure, and let small derivation mean that the derivation satisfies the corresponding smallness condition. The model-completeness conjecture. The theory of the ordered differential field $\mathbb{T}$ is model complete, and is the model companion of the theory of $H$-fields with small derivation. This is the main model-theoretic problem for transseries described in the paper; the supplied text gives no evidence that it has been resolved.