Conjecture on initial degrees of symbolic powers of general point sets

Let $Z\subset\mathbb{P}^n$ be a set of $n+3$ points in linearly general position, with $n$ odd, and let $I_Z$ be its homogeneous ideal. For a homogeneous ideal $J$, let $\alpha(J)$ be the least degree of a nonzero homogeneous element of $J$. Symbolic-power initial-degree conjecture. For every $k\geq1$,

$$\alpha(I_Z^{(k)})=\left\lceil\frac{(n+1)(n+3)k}{n^2+2n-1}\right\rceil.$$

This removes an assumption from the paper's preceding theorem and would determine all initial degrees of symbolic powers for these point configurations. The paper proves related formulas and identifies this assertion as an expected extension; the full statement remains open.