Conjecture on admissible pictures and Littlewood–Richardson crystals

Let $\lambda$, $\mu$, and $\nu$ be Young diagrams with $|\lambda|+|\mu|=|\nu|$. Let $A$ be an admissible order on the skew Young diagram $\nu\setminus\lambda$, and let $A'$ be an admissible order on $\mu$. Write $\mathbf{P}(\mu,\nu\setminus\lambda;A,A')$ for the set of admissible pictures and $\mathbf{B}(\mu)^\nu_\lambda[A']$ for the Littlewood–Richardson crystal associated with $A'$. Admissible-pictures conjecture. There exists a bijection

$$\Psi:\mathbf{B}(\mu)^\nu_\lambda[A']\longrightarrow \mathbf{P}(\mu,\nu\setminus\lambda;A,A').$$

This conjecture seeks to generalize the known correspondence between ordinary pictures and Littlewood–Richardson crystals to arbitrary admissible orders. Its status is not determined by the supplied source context.