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The recursive spectrum of a fixed strongly minimal theory T is the set of integers n such that the model of T of dimension n admits a recursive presentation. How complicated can this set be? Some interesting examples can be constructed by coding complicatedness into an infinite language, or by using Hrushovski constructions. We are working towards showing that the recursive spectrum of a strongly minimal locally modular theory in finite language must be nothing; everything; or only the prime model. The title describes the current state of this joint work with Uri Andrews.