The logarithmic list-replicability conjecture for sign matrices

Let $A$ be an $N \times M$ sign matrix, and let $\operatorname{\textnormal{\textsc{lr}}}(A)$ denote its list replicability number. List-replicability conjecture. Every $N \times M$ sign matrix $A$ satisfies

$$\operatorname{\textnormal{\textsc{lr}}}(A) = O(\log N \log M).$$

The conjecture asserts that list replicability is at most logarithmic in each matrix dimension. Originally posed in, it was resolved for extremal concept classes in, where $\operatorname{\textnormal{\textsc{lr}}}(\mathcal{C}) = \Theta(\operatorname{\textnormal{\textsc{vc}}}(\mathcal{C}))$ was shown.