Affine crystal isomorphism conjecture for type D4^(3) rigged configurations

Let

$$B=\bigotimes_{k=1}^N B^{r_k,s_k}$$

be a tensor product of type $D_4^{(3)}$ KR crystals, and let $\operatorname{RC}(B)$ be its rigged-configuration set equipped with the conjectural affine crystal operators. Affine rigged-configuration conjecture. There exists an affine crystal isomorphism

$$\Phi:\operatorname{RC}(B)\longrightarrow B.$$

This strengthens the set-theoretic bijection and statistic-preservation conjecture by requiring compatibility with the full affine crystal structure.