TL-pfaffinant Schur Q-positivity conjecture

Let $P_n$ be the algebra containing the element $f$, let $\mathrm{Pfaf}'_D$ denote the diagram pfaffinants, and let $A_{\lambda/\mu}$ be a generalized $Q$-Jacobi-Trudi matrix associated with a skew shifted shape $\lambda/\mu$. Suppose

$$f=\sum_D c_D\mathrm{Pfaf}'_D,$$

where each $c_D$ is non-negative. TL-pfaffinant Schur $Q$-positivity conjecture. For every generalized $Q$-Jacobi-Trudi matrix $A_{\lambda/\mu}$, the evaluation $f(A_{\lambda/\mu})$ is a nonnegative linear combination of Schur $Q$-functions. This conjecture proposes a connection between decompositions into diagram pfaffinants and Schur $Q$-positivity; its resolution is not given in the source.