The crystal-bijection and cocharge conjecture for rigged configurations

Let $B = \bigotimes_{k=1}^N B^{r_k,s_k}$ be a tensor product of Kirillov–Reshetikhin crystals. Let $\operatorname{RC}(B)$ denote the corresponding set of rigged configurations, let $\Phi\colon \operatorname{RC}(B)\to B$ be the proposed crystal bijection, let $\theta$ send every rigging to its corresponding corigging and extend as a classical crystal isomorphism, let $\operatorname{cc}$ denote cocharge, and let $D$ denote the associated energy statistic.

Crystal-bijection and cocharge conjecture. The map $\Phi$ is a classical crystal isomorphism and satisfies

$$\operatorname{cc}=D\circ\Phi\circ\theta.$$

The statement packages the expected compatibility between rigged configurations, tensor-product crystals, cocharge, and energy. The source introduces it among conjectural properties of the bijection and gives no resolution for the full stated generality.