Newell–Littlewood saturation conjecture

Let ${\operatorname{Par}}_n$ denote the set of partitions with at most $n$ parts, and let $N_{\lambda,\mu,\nu}$ be the Newell–Littlewood coefficient for $(\lambda,\mu,\nu)\in({\operatorname{Par}}_n)^3$. Then $N_{\lambda,\mu,\nu}\neq 0$ if and only if $|\lambda|+|\mu|+|\nu|$ is even and there exists $t>0$ such that

$$N_{t\lambda,t\mu,t\nu}\neq 0.$$

NL-saturation conjecture. The stated equivalence holds for every $(\lambda,\mu,\nu)\in({\operatorname{Par}}_n)^3$. This is the proposed analogue of the Littlewood–Richardson saturation theorem for Newell–Littlewood coefficients; the source presents it as a generalization, and no resolution is supplied here.