Surjectivity of the map from prime characteristics to maximal Frobenius distance

Determine whether the map p↦δ(p), where δ(p) is the maximum over supersingular elliptic curves in characteristic p of the least degree of an isogeny to the Frobenius conjugate, is surjective onto the positive integers, thereby resolving the conjectured surjectivity of p↦δ(p).

Background

The paper proves that every prescribed positive integer occurs as δ_E for some supersingular elliptic curve in infinitely many prime characteristics, and that finite collections of prescribed δ_E-values can occur simultaneously in one characteristic. These results establish lower bounds for δ(p), but they do not control the maximum over all supersingular curves in that characteristic.

The unresolved issue is whether every positive integer is actually attained by δ(p) itself for some prime p, rather than merely by an individual curve invariant δ_E. The paper explicitly identifies this as the conjectured surjectivity problem from the cited earlier work.