Late Roman Unit Sizes

[Nathan Ross]

The Notitia clearly makes a distinction between units called Numeri, Legiones, Alae, Cohortes, and Cunei

Maybe it does, but that distinction doesn't seem to be borne out by other evidence from around the same period! The units of palatine auxilia listed in the ND are described as numeri on the Concordia tombstones (and in other inscriptions); the Perge inscription describes a legion as a numerus... Literary sources call all sorts of units numeri.

There were older units (2nd-3rd C) that were solely called numeri - usually frontier formations, perhaps more or less irregular - and some of these may have metamorphosed into new-style auxilia at some point. But it seems likely that, by the later empire, the word was being used for all other sorts of military unit as well...

So unless every unit in the late Roman army was the same size, I don't think we can assume that the word numerus or arithmos connoted a fixed number of men.