Polishchuk–Positselski's generator conjecture for Koszul algebras

Let $A$ be a Koszul algebra with finite global dimension $n$.

Polishchuk–Positselski's conjecture. The algebra $A$ has at least $n$ generators.

This conjecture was proposed by Polishchuk and Positselski and is refuted by the algebra $A=\bfk \la x,y,z \ra/(x^{2}+yx,xz,zy)$ introduced by Iyudu and Shkarin, which provides a counterexample.