Surjectivity conjecture for the minimal isogeny degree of supersingular elliptic curves

Let $\mathcal{E}$ be the set of isomorphism classes of supersingular elliptic curves defined over $\overline{\mathbb{F}}_p$ for all primes $p$, and let $\delta\colon\mathcal{E}\to\mathbb{Z}_{>0}$ assign to each class represented by $E$ the value $\delta_E$. Surjectivity conjecture. For every $n\in\mathbb{Z}_{>0}$, there exists an $E$ with $\delta_E=n$, equivalently,

$$\operatorname{Im}(\delta)=\mathbb{Z}_{>0}.$$

The claim says that every positive integer occurs as the minimal degree of an isogeny associated with some supersingular elliptic curve. It is supported by the paper's computational data but remains unproved.