3-Schur property for Lipschitz-free spaces over complete purely 1-unrectifiable metric spaces

Determine whether, for every complete purely 1-unrectifiable metric space M, the Lipschitz-free space F(M) has the 3-Schur property.

Background

The main result of the paper proves that Lipschitz-free spaces over uniformly discrete metric spaces are 3-Schur and shows the constant 3 is optimal in that class. For proper purely 1-unrectifiable spaces, a stronger 1-Schur result is known. The authors ask whether the 3-Schur conclusion extends to all complete purely 1-unrectifiable spaces, which need not be uniformly discrete nor proper.

References

The following problem remains open.

Assume $M$ is a complete purely $1$-unrectifiable metric space. Is $(M)$ $3$-Schur?

— Lipschitz-free spaces over uniformly discrete metric spaces are 3-Schur  (2604.01875 - Cúth et al., 2 Apr 2026) in Introduction, Question (following Theorem 1.1)