Primitive recursive categoricity spectra of functional structures

For the notion of degree of categoricity, we study an analogous notion for punctual structures. We show that such notions coincide for non-${\mathrm{\Delta }}_1^0$-categorical injection structures, and construct an example of a ${\mathrm{\Delta }}_1^0$-categorical injection structure for which these notions differ. Additionally, we also show that in every non-zero c.e.~Turing degree, there exists a PR-degree that is low for punctual isomorphism (to be defined), and also a PR-degree that is a degree of punctual categoricity.