Positive-dimensional recursive model conjecture for strongly minimal theories

Let $T$ be a strongly minimal theory in a finite signature satisfying the Zilber Trichotomy. A model $M\models T$ is positive dimensional if its dimension is greater than zero, and a structure is recursive if its atomic diagram is recursive.

Positive-dimensional recursive model conjecture. If some positive-dimensional model $M\models T$ is recursive, then all models of $T$ are recursively presentable.

This is presented as a stronger version of the recursive-spectrum trichotomy conjecture. The source does not provide a resolution; related cases are known for disintegrated theories and for field-like theories with classical Zariski geometries, while the general statement remains open.