3-Schur property for Lipschitz-free spaces over snowflaked Banach spaces

Determine whether, for an infinite-dimensional Banach space X and p in (0,1) with the snowflake metric d(x,y) = ||x−y||^p, the Lipschitz-free space F(X,d) has the 3-Schur property.

Background

The authors consider snowflaked metrics on Banach spaces, which often alter geometric and Lipschitz properties significantly. They ask whether the 3-Schur property holds for Lipschitz-free spaces over such snowflaked versions of infinite-dimensional spaces like ℓ1, c0, or ℓ2.

References

In particular, the following special cases remain open.

(ii) Let $X$ be an infinite-dimensional Banach space (for example $X=\ell_1$, $X=c_0$ or $X=\ell_2$). Let $p\in (0,1)$. Define a new metric on $X$ by $d(x,y)=|x-y|p$, $x,y\in X$. Is $(X,d)$ $3$-Schur?

— Lipschitz-free spaces over uniformly discrete metric spaces are 3-Schur  (2604.01875 - Cúth et al., 2 Apr 2026) in Introduction, Question (special cases remain open), item (ii)