Knutson's K-theoretic geometric Littlewood–Richardson conjecture

Let $X_1$ and $X_2$ be the two components arising when a puzzle variety breaks in the geometric Littlewood–Richardson degeneration, and let $X_3$ be the puzzle variety corresponding to the third, K-theoretic option. K-theoretic geometric Littlewood–Richardson conjecture. $X_3$ is a $GL(n)$-translate of the scheme-theoretic intersection $X_1\cap X_2$. This conjecture gives a geometric explanation of the subtraction term in Buch's K-theoretic Littlewood–Richardson rule, since a scheme-theoretic degeneration into two components contributes the intersection with negative sign in K-theory.