The tableau-process weight conjecture for general multiline diagrams

Let the vertex model $\mathfrak{Q}^{\mathrm{qBos}}(\mathbf{u};\mathbf{1};\mathbf{0})$ be defined on the cylinder, with no restrictions on the number of particles of each color. Each vertex-model configuration determines a multiline diagram, possibly non-injectively. Define the weight of a multiline diagram as the sum of the weights of all corresponding vertex-model configurations over the winding of paths around the cylinder.

Tableau-process weight conjecture. This weight is proportional to the weight derived from the tableau process of Ayyer et al.

This conjecture proposes that the vertex-model construction extends the tableau-process stationary weights to the general case of unrestricted particle numbers, despite the many-to-one correspondence between configurations and multiline diagrams.