Fox–Li conjecture for edge-ordered Ramsey numbers of degenerate graphs

Let $H^\prec$ be an edge-ordered $d$-degenerate graph on $n$ vertices, and let $R_\prec(H^\prec)$ be its edge-ordered Ramsey number. Fox–Li conjecture. One has

$$R_\prec(H^\prec)\leq n^{O(d)}.$$

This would improve the known bound $R_\prec(H^\prec)\leq n^{600d^3\log(d+1)}$ for edge-ordered $d$-degenerate graphs. The source further says that no examples with superlinear edge-ordered Ramsey numbers are known, while Fox and Li conjectured that the displayed upper bound is tight up to the constant in the exponent.