The positivity conjecture for K-orbit multidegrees

Let $\gamma$ be a clan and let $\Upsilon_{\gamma}(X;Y)$ denote the polynomial associated to the $K$-orbit closure $Y_{\gamma}$. K-orbit multidegree conjecture. Theorem~(III) holds for all $\gamma$. The supplied evidence states that this assertion has been verified by exhaustive computer checks through $p+q=7$; its general validity is therefore recorded as solved only in those checked cases, not as a proof of the universal statement.