I will discuss joint work with E. Panzer on the `completion conjecture' which relates point counts mod q of graph hypersurfaces over finite fields F_q. To tackle it involves studying a general family of Mellin transforms, their P-recurrences, tropical and Apery limits, and studying points over finite fields of hypersurfaces modulo prime powers. When applied to graph hypersurfaces, this formalism reproduces a number of diverse combinatorial invariants of graphs, and organises them into a single invariant.