Tree dichotomy for slalom-based eventually different families

Establish whether analytic $\not\ni^*$-dominating families satisfy a tree dichotomy.

Background

The paper studies a slalom-based eventually different forcing associated with an analytic $P$-ideal and proves that it has the total universality property and is proper. The authors ask whether the analytic dominating families arising from this relation admit a structural tree dichotomy analogous to dichotomies known in related settings.