Sup-polynomial emergence conjecture

Let $M$ be the compact manifold under consideration, and let $\operatorname{Diff}(M)$ denote its diffeomorphism space. Sup-polynomial emergence conjecture. There exists an open set $U\subset \operatorname{Diff}(M)$ such that a typical $f\in U$ has emergence of type Sup-P. The source contrasts this with familiar systems whose emergence is at most polynomial and proposes that systems with sup-polynomial emergence occur non-negligibly in an open set. The precise definition of typicality and the notation Sup-P are given elsewhere in the source; no resolution is supplied.