Expected-codimension conjecture for Weddle schemes of general points

Let $d\geq 3$ and let $Z$ be a set of $\binom{d+2}{2}-1$ general points in $\mathbb{P}^3$. The $d$-Weddle scheme of $Z$ is the scheme associated to the loci of points from which the projection of $Z$ satisfies the relevant degree-$d$ condition. Expected-codimension conjecture. The $d$-Weddle scheme of $Z$ has the expected codimension, namely $2$. The proposition preceding this conjecture establishes the consequence that, when this expected codimension holds, the scheme is an ACM curve of degree $\binom{\binom{d+2}{3}+1}{2}$ containing the lines joining pairs of points of $Z$; the conjecture itself is asserted for general $d$ and remains unresolved in the supplied text.