DP-completeness of exact circular chromatic index

Let $r\ge 3$ be a rational number. For a graph $G$, let $\chi_c'(G)$ denote its circular chromatic index, and let $\mathrm{CCHI}^{=_r}$ be the decision problem of determining whether $\chi_c'(G)=r$.

DP-completeness conjecture. The problem $\mathrm{CCHI}^{=_r}$ is DP-complete.

The preceding complexity discussion establishes NP-completeness for deciding whether $\chi_c'(G)\le r$ and explains why exact equality also involves a coNP component; the claimed DP-completeness is proposed on that basis.