Combined injectivity conjecture for rack homology operations on odd dihedral quandles

Let $R_k$ be an odd dihedral quandle, and let $(h'_0)_*$ and $(h_s)_*$ be the induced homology operations

$$(h'_0)_*:H_{n+1}^R(R_k)\longrightarrow H_{n+2}^R(R_k),$$ $$(h_s)_*:H_n^R(R_k)\longrightarrow H_{n+2}^R(R_k).$$

Combined injectivity conjecture. For odd $k$ and $n>1$, the direct-sum map

$$(h'_0)_*\oplus(h_s)_*:H_{n+1}^R(R_k)\oplus H_n^R(R_k)\longrightarrow H_{n+2}^R(R_k)$$

is a monomorphism. This strengthens the separate injectivity expectations for the two rack-homology operations introduced in the paper; it is presented as a future direction and remains open.