Polishchuk–Positselski rationality conjecture for Koszul algebras

Let $A$ be a finitely generated Koszul algebra. Its Hilbert series is the formal power series encoding the graded dimensions of $A$.

Polishchuk–Positselski conjecture. The Hilbert series of $A$ is a rational function.

This conjecture concerns the expected algebraic simplicity of Hilbert series for finitely generated Koszul algebras and is stated in the source as still open. The paper uses it as motivation for analogous conjectures for Koszul operads.