Leibman's conjecture on polynomial nilmanifold orbit averages

Let $W=N/\Lambda$ be a connected nilmanifold, let $Y=\pi(H)$ be a connected subnilmanifold of $W$, where $H$ is a connected closed subgroup of $N$ and $\pi:N\to W$ is the quotient map. Let $g:\mathbb Z\to N$ be a polynomial sequence with $g(0)=\operatorname{Id}_N$ such that $g(\mathbb Z)Y$ is dense in $W$, and assume that $N$ is generated by its connected component $N^o$ and the elements of $g$. Let $Z$ be the normal closure of $Y$ in $W$. Leibman's conjecture. For every $f\in C(W)$,

$$\lim_{n\to\infty}\left(\int_{g(n)Y}f\,d\mu_{g(n)Y}-\int_{g(n)Z}f\,d\mu_{g(n)Z}\right)=0.$$

The paper's appendix is explicitly devoted to disproving this conjecture, so the asserted statement is refuted by the paper's example.