Fractional coloring conjecture for degenerate triangle-free hypergraphs

Let $H$ be an $r$-uniform $d$-degenerate triangle-free hypergraph, with $r\geq 3$. Here, $\chi_f(H)$ denotes the fractional chromatic number, and $c_r>0$ is a constant depending on $r$. Fractional coloring conjecture. There is a constant $c_r>0$ such that

$$\chi_f(H) \leq c_r\left(\frac{d}{\log d}\right)^{\frac{1}{r-1}}.$$

This conjecture extends the known chromatic-number bound for triangle-free uniform hypergraphs to fractional coloring, replacing maximum degree by degeneracy. Its status is open.