Regularity of good even-characteristic pseudo-ovoids

Determine whether every good pseudo-ovoid in PG(4n − 1, q) for even q is regular.

Background

Goodness is a local incidence property of a pseudo-ovoid. The paper proves several consequences of goodness, including regularity under additional assumptions concerning pseudo-ovals through a fixed element. It leaves open whether goodness alone forces regularity in even characteristic.

References

Open problem 11. For q even, is every good pseudo-ovoid O of PG(4n − 1, q) regular?

Arcs, Caps and Generalisations in a Finite Projective Space  (2503.06243 - Hirschfeld et al., 8 Mar 2025) in Open problem 11, Section 8.6, page 8