Characterization of strongly minimal hyperfields

A hyperfield is a field-like structure with multivalued addition, and its hyperaddition is this multivalued addition; its multiplicative group is the group formed by its nonzero elements under multiplication. A structure is strongly minimal when every definable subset of its universe is finite or cofinite.

Strong minimality conjecture. A hyperfield is strongly minimal if and only if it is either a strongly minimal field, that is, an algebraically closed field, or a hyperfield whose hyperaddition is definable in the structure of its multiplicative group, with that multiplicative group strongly minimal.

This proposes a model-theoretic classification of the simplest hyperfields. The source presents it as a proposal, and no resolution is supplied here.