Tree dichotomy for slalom localization families

Establish whether analytic $\subseteq_{\operatorname{sl}^*}$-dominating families satisfy a tree dichotomy.

Background

The paper analyzes slalom localization forcing, proves its total universality and properness, and relates it to increasing the cardinal invariant $\add(\mathcal{N})$. It leaves open whether the corresponding analytic dominating families have a tree-based dichotomy.

References

Is there a tree dichotomy for the analytic $\subseteq_{\operatorname{sl}*$-dominating families?

— Universal domination and idealized forcing  (2608.18964 - Schilhan, 19 Aug 2026) in Question in Section 6, subsection “Slalom based localization forcing”