Universal behaviour of generalized Causal set d'Alembertians in curved spacetime

Causal set non-local wave operators allow both for the definition of an action for Causal set theory and the study of deviations from local physics that may have interesting phenomenological consequences. It was previously shown that, in all dimensions, the (unique) minimal discrete operators give averaged continuum non-local operators that reduce to $\Box-R/2$ in the local limit. Recently, dropping the constraint of minimality, it was shown that there exist an infinite number of discrete operators satisfying basic physical requirements and with the right local limit in flat spacetime. In this work, we consider this entire class of Generalized Causal set d'Alembertins in curved spacetimes and extend to them the result about the universality of the $-R/2$ factor. Finally, we comment on the relation of this result to the Einstein Equivalence principle.