The conjectural evaluation formula for Jack superpolynomials

Let $\Lambda$ be a superpartition, let ${P}^{(\alpha)}_\Lambda$ be the corresponding Jack superpolynomial in the $M$-fermionic sector, and let $N\geq\ell(\Lambda)$. Let $\Delta\Lambda=\Lambda^{[3]}/\delta_{\overline m,\underline m}$ be the skew diagram obtained by removing the fermionic core $\delta_{\overline m,\underline m}$, let $B_i\Lambda$ be the four subsets of bosonic boxes, and let $\xi_{\overline{\underline{\Lambda}}}$ denote the normalization factor. For a box $s=(i,j)$ in a partition $\lambda$, define the co-arm and co-leg lengths by

$$a'_\lambda(s)=j-1,\qquad \ell'_\lambda(s)=i-1.$$

The evaluation conjecture. The evaluation of the Jack superpolynomial is

$$E_{N,M}\left[{P}^{(\alpha)}_\Lambda\right]=\binom{N-\overline m-\underline m}{\overline{\underline m}}^{-1}\frac{\displaystyle\prod_{s\in\Delta\Lambda}\left(N-\ell'_{\Lambda^{[3]}}(s)+\alpha a'_{\Lambda^{[3]}}(s)\right)}{\displaystyle\xi_{\overline{\underline{\Lambda}}}\prod_{i=0}^{3}\prod_{s\in B_i\Lambda}\left(\ell_{\Lambda^{[i]}}(s)+1+\alpha a_{\Lambda^{[3]}}(s)\right)}.$$

Here $E_{N,M}$ is the evaluation functional defined using the fermionic scalar product and the relevant Vandermonde factors. The expression is presented as conjectural in the supplied text, and no proof or resolution is given there.