Recursive-spectrum trichotomy conjecture for strongly minimal theories

Let $T$ be a strongly minimal theory in a finite signature satisfying the Zilber Trichotomy. Its recursive spectrum is the set of dimensions of countable models of $T$ that are recursively presentable.

Recursive-spectrum trichotomy conjecture.

$$\operatorname{SRM}(T)\in\{\emptyset,\omega+1,\{0\}\}.$$

Equivalently, all countable models of $T$ are recursively presentable, none are recursively presentable, or only the zero-dimensional model is recursively presentable. The conjecture remains open for finite covers of groups and fields.