Niebrzydowski–Przytycki injectivity conjecture for the quandle homology operation $h_s$

Let $R_k$ be the dihedral quandle of odd prime order $k$, and let $h_s$ be the degree-two chain map inducing

$$(h_s)_*:H_n^Q(R_k)\longrightarrow H_{n+2}^Q(R_k).$$

Injectivity conjecture for $h_s$. For $n>1$, the homomorphism

$$h_s:H_n^Q(R_k)\longrightarrow H_{n+2}^Q(R_k)$$

is a monomorphism. The paper proves that the corresponding map from $H_1^Q(R_k)$ onto $H_3^Q(R_k)$ is an epimorphism, but does not establish this higher-degree injectivity statement.