The optimal dimension bound for higher-order GJMS Aubin sets

Let $k,m\in\mathbb{N}$ and let $N(k,m)$ be the dimension threshold appearing in the higher-order GJMS geometric Aubin set conjecture for conformal manifolds virtually conformal to an $m$-special Einstein product. The optimal dimension conjecture.

$$N(k,m)=2k+2m-1.$$

This would identify the optimal dimension threshold in the partial result for manifolds virtually conformal to an $m$-special Einstein product. The source presents it as a specialization of the preceding conjecture; no resolution is supplied.