Degree conjecture for degenerate sphere maps

Let $H:\mathbb{S}^{2n-1}\rightarrow\mathbb{S}^{2N-1}$ be a sphere map with linearly independent components, and let $s>0$. Degree conjecture. If $H$ is $s$-degenerate, then $H$ has degree $N-s-1$. This proposes a general degree formula for positively degenerate sphere maps, extending the quadratic conclusion established in the preceding theorem for constantly $(N-3)$-degenerate maps from $\mathbb{S}^{3}$ under its stated non-containment hypothesis; the conjecture is presented without a resolution in the source.