Halliday & Matthiessen (1999: 450):
More generally, the Medium is related as a member of a set, which is defined either by a quality or by a class. The relation is a composite of the participants (the Carrier and the Attribute) and the nuclear relation. The nuclear relation is not necessarily a state; it can be either a being or a becoming, both of which are located in time, as are processes in general.
But its participants are static things; the Carrier is an individual or class, and the Attribute is a lasting quality or a wider class. The Attribute of the relation of becoming applies to the Carrier in the final state of the becoming; it is a resultative Attribute.