The distinguishing proper arc-colouring conjecture for complete symmetric digraphs

Let $\overleftrightarrow{K_n}$ be the complete symmetric digraph on $n$ vertices. Write $\chi'_{D_{2}}(\overleftrightarrow{K_n})$ for its distinguishing proper arc-colouring number, and let $\chi'_{2}(\overleftrightarrow{K_m})$ denote the corresponding proper arc-colouring number under the paper's type-II condition. The distinguishing proper arc-colouring conjecture.

$$\chi'_{D_{2}}(\overleftrightarrow{K_{n}}) = \chi'_{2}(\overleftrightarrow{K_{\lceil\frac{n}{2}\rceil}})+1.$$

This conjecture predicts that the distinguishing number for complete symmetric digraphs is obtained from the type-II parameter at half the order, with one additional colour. Its status is not resolved in the supplied source context.