Optimal quantitative WSC constant for Lipschitz-free spaces over uniformly discrete metric spaces

Determine the optimal constant C such that every Lipschitz-free space over a uniformly discrete metric space is C-WSC, given that the current results imply the bound C=3.

Background

The authors discuss quantitative weak sequential compactness (C-WSC) and note that many Lipschitz-free spaces enjoy WSC. Using their main theorem and known results, they conclude that Lipschitz-free spaces over uniformly discrete spaces are 3-WSC. However, they point out that the optimal constant is unknown, even in this setting.

References

Indeed, by Theorem~\ref{T:main} and Proposition 1.1, Lipschitz-free spaces over uniformly discrete spaces are $3$-WSC, but it is not clear whether this constant is optimal.

— Lipschitz-free spaces over uniformly discrete metric spaces are 3-Schur  (2604.01875 - Cúth et al., 2 Apr 2026) in Introduction, paragraph on quantitative weak sequential compactness (WSC) near the end