3 problems

Failure of general universal consistency conjecture. As in the Wasserstein case, universal consistency of $k_n$-NN will not hold in full generality.

Bounded VCN-dimension conjecture. The resulting hypothesis class should have bounded $\operatorname{VCN}_{2,2}$-dimension.

Let $X$ be the random element under study, let $\Pi^q X$ denote its $q$-dimensional score vector, and let $L_n^q$ be the maximum nearest-neighbor indegree among the corresponding s…