Stanley-sum rule conjecture for Jack Littlewood–Richardson coefficients

For partitions $\mu,\nu,\lambda$, let $\mathsf{SD}_{\mu\nu}^{\lambda}$ be the set of Stanley diagrams and let a Stanley sum be an integer linear combination of these diagrams. Stanley-sum rule conjecture. For every triple of partitions, there exists a Stanley sum

$$\bm g_{\mu\nu}^{\lambda}=\sum_{\bm D\in\mathsf{SD}_{\mu\nu}^{\lambda}}c_{\bm D}\bm D,\qquad c_{\bm D}\in\mathbb Z,$$

whose evaluation gives the corresponding Jack Littlewood–Richardson coefficient:

$$g_{\mu\nu}^{\lambda}=[\bm g_{\mu\nu}^{\lambda}].$$

Such a Stanley sum is called a rule for $g_{\mu\nu}^{\lambda}$. It generalizes the strong Stanley conjecture from Littlewood–Richardson multiplicity one to arbitrary triples; the source attributes this generalization to earlier work and gives no resolution evidence.