The optimal labeling conjecture for bounded twin-width classes

Let $\mathcal C$ be a graph class, and let an $f(n)$-bits adjacency labeling scheme assign labels of length at most $f(n)$ to the vertices of every $n$-vertex graph in $\mathcal C$, with a fixed decoder determining adjacency from two labels. A class has bounded twin-width if the twin-widths of its graphs are bounded by a constant.

Optimal labeling conjecture. Every bounded twin-width class has a $(1+o(1))\log n$-bits labeling scheme.

The paper presents this as a conjectural improvement of its labeling theorem, aiming for optimality up to the second-order term. No resolution is given in the supplied text.