By this definition there are hundreds or thousands of SoM. Each quantum hall regime is a SoM different nuclear pasta are SoM, every distinct crystal reconfiguration is a SoM. And, I suspect, topological edge modes are also a SoM as claimed by Microsoft

This is commonly extended to mean, if there is a phase transition then there are two distinct SoMs. Phase transition meaning a discontinuous change in some trait of the system. That means that while you vary some external parameter the system goes through a distinct change

If you want to stretch the concept of "state of matter" (SoM) to broad discussions like this it requires careful rethinking of definitions. Wikipedia lists SoM as "one of the distinct forms in which matter can exist". en.m.wikipedia.org/wiki/State_o...

This article doesn't include a definition of what a "state of matter" is? As always it is well written, and gives a nice and accurate description of the 7 systems considered. But I disagree with the conclusion of the article.