Deery–Geramita conjecture on catalecticant minors

Let $V$) be a finite-dimensional vector space, and let $\Upsilon^{i,d-i}$ denote the corresponding catalecticant map; write $\operatorname{Minors}_r(\Upsilon^{i,d-i})$ for the ideal generated by its $r\times r$ minors. Deery–Geramita conjecture. The ideal

$$\operatorname{Minors}_r(\Upsilon^{i,d-i})$$

is saturated for any $r$, $d$, and $i$. This concerns the scheme-theoretic structure of catalecticant loci and is motivated by questions posed by Geramita; the source gives no resolution status.