Recurrence transfer conjecture for nilsystems

Let $s\geq 1$, and let $R\subset\mathbb N$ be a set of $s$-recurrence for $s$-step nilsystems. Recurrence transfer conjecture. Then $R$ is a set of $s$-recurrence for all $t$-step nilsystems for any $t\geq s$. This conjecture asks whether recurrence for systems of the same step automatically persists for nilsystems of every higher step; the source gives no resolution beyond the related cases discussed immediately before the conjecture.