W[1]-hardness of M-EPVCB parameterized by the smaller bipartition

Let $G=(X,Y,E)$ be the edge-weighted bipartite graph in an instance of M-EPVCB, and let $|X|$ and $|Y|$ denote the sizes of its two bipartition classes. The minimum-side hardness conjecture. M-EPVCB is W[1]-hard with respect to the parameter $\min\{|X|,|Y|\}$. This would strengthen the known W[1]-hardness result parameterized by $k_1$; the conjecture is posed as a question for future work and remains unresolved in the supplied source.