I think I might have stumbled upon a new category of common properties here. (At least new to me.) Basically, test that some subset of your output variables is a function of a specific subset of your input variables. And conversely, test that some subset of your output variables is independent (under some conditions) of some subset of your input variables.

My go-to example for property based testing isn't addition, but idempotence. Idempotence is a concept well known from REST apis to the general programming public, and also in sorting or clean up data. And it's easy to state in code, eg: sorted(sorted(x)) == sorted(x).