Shifted Fomin–Fulton–Li–Poon Schur Q-positivity conjecture

For two shifted shapes $\lambda$ and $\mu$, let $\lambda\cup\mu$ be the partition obtained by rearranging all parts of $\lambda$ and $\mu$ in weakly decreasing order, and write

$$\lambda\cup\mu=(\nu_1,\nu_2,\nu_3,\ldots).$$

Define $\mathrm{sort}_1(\lambda,\mu)=(\nu_1,\nu_3,\nu_5,\ldots)$ and $\mathrm{sort}_2(\lambda,\mu)=(\nu_2,\nu_4,\nu_6,\ldots)$. Shifted Fomin–Fulton–Li–Poon conjecture. The difference

$$Q_{\mathrm{sort}_1(\lambda,\mu)}Q_{\mathrm{sort}_2(\lambda,\mu)}-Q_\lambda Q_\mu$$

is a nonnegative linear combination of Schur $Q$-functions. The claim is presented as the shifted analogue of a Schur-function positivity theorem and is not resolved in the source.