Knutson's two-step Littlewood–Richardson puzzle conjecture

Let $\alpha$, $\beta$, and $\gamma$ be strings indexing Schubert classes in the two-step flag variety, and let $c^{\gamma}_{\alpha,\beta}$ denote the corresponding two-step Littlewood–Richardson number. Knutson's two-step Littlewood–Richardson puzzle conjecture. The number $c^{\gamma}_{\alpha,\beta}$ equals the number of puzzles with sides $\alpha$, $\beta$, and $\gamma$, filled with the puzzle pieces specified in the source. This conjecture generalizes the geometric Littlewood–Richardson puzzle rule from the Grassmannian to two-step flag varieties; the supplied text does not state a resolution.