Gasca–Maeztu conjecture for $GC_n$ sets

Let a $GC_n$ set be an $n$-correct set $\mathcal{X}$ in which the fundamental polynomial of every node is a product of $n$ linear factors. Gasca–Maeztu conjecture. Any $GC_n$ set contains $n+1$ collinear nodes. The case $n=3$ was established by M. Gasca and J. I. Maeztu; the general statement is the subject of the conjecture.