The sparse-graph reformulation of the fractional expectation threshold conjecture

For $q\in[0,1]$, call a graph $J$ $q$-sparse if

$$\mathbb{E}_qX_I\geq 1\quad\forall I\subseteq J,$$

where $\mathbb{E}_qX_I$ is the expected number of copies of $I$ in $G_{n,q}$. Sparse-graph reformulation. There is a fixed $K$ such that if $H$ is $q$-sparse and $p=Kq$, then

$$N(H,F)<\mathbb{E}_pX_F\quad\forall F\subset H.$$

This is stated as an appealing restatement of the fractional expectation threshold conjecture, with the harmless convention change from threshold $1/2$ to $1$ noted in the source. It is therefore open together with that conjecture.