An optimality-theoretic (OT) system is specified by defining its constraints and the structures they evaluate. These give rise to a set of grammars, the typology of the system, which emerges from the often complex interactions among constraints and structures. Every typology is determined by a finite collection of candidate sets (csets). How do we know that we have assembled a universal support, a collection of csets sufficient to distinguish all grammars of the system? Lacking a universal support, we do not have the typology and we cannot deal systematically with its structure and consequences.
This concrete question can be answered in terms of an enhanced abstract understanding of typological structure. Under property theory (Alber & Prince 2015a,b), a typology is resolved into a set of properties: ranking conditions that have mutually exclusive values. When the structural correlates of each value are determined, the ranking values defining a grammar also determine the extensional traits exhibited in its optima. Suppose we have the property analysis of a typology derived from a proposed support for an OT system. If every consistent choice of values ensures that a single optimum is chosen in every cset admitted by the system, then no grammar derived from the proposed support can be split by consideration of further csets, and that support must be universal for the system. This method of proof is applicable to any OT system. Here we use it to analyze the prosodic system nGX (Alber & Prince 2015b), determining its universal supports and the shape of the forms made optimal by its grammars.