Shangguan's generic Vandermonde full-rank conjecture

Let $[t]=\{1,\ldots,t\}$ and let $J_1,\ldots,J_t\subseteq[n]$ satisfy, for every $S\subseteq[t]$,

$$\sum_{i\in S}|J_i|-\left|\bigcup_{i\in S}J_i\right|\leqslant (|S|-1)k.$$

Assume also that the corresponding inequality is an equality for $S=[t]$. Let $G$ be a generic $(n,k)$-Vandermonde matrix, and let $M_{G,(J_1,\ldots,J_t)}$ be the matrix defined in the source from $G$ and these subsets.

Shangguan's full-rank conjecture. The matrix $M_{G,(J_1,\ldots,J_t)}$ has full column rank.

The conjecture is formulated as a rank criterion whose resolution would imply that generic Reed–Solomon codes achieve list-decoding capacity. The source does not provide evidence of a resolution, so its status is open.