The defining-relations conjecture for truncated shifted iYangians

Let $\tau$ be the diagram involution, let $\bar{\mathbf{v}}_j$ denote the associated class of the dimension vector at $j$, and let $\bm z$ be the central parameters. For a dominant $\tau$-invariant coweight $\lambda$, an even spherical coweight $mu$ with $\lambda\geqslantmu$, and the iGKLO epimorphism

$$\Phi_{\mu}^{\lambda}:{^{\imath}\mathcal{Y}}_{\mu}[\bm z]\twoheadrightarrow {^{\imath}\mathcal{Y}}_{\mu}^{\lambda},$$

write $\mathsf A_i(u)=1+\sum_{r>0}\mathsf A_i^{(r)}u^{-r}$ and $\mathsf B_i(u)=u^{\mathbf{v}_i}\sum_{r>0}\mathsf B_i^{(r)}u^{-r}$. The defining-relations conjecture. There is an isomorphism

$${^{\imath}\mathcal{Y}}_\mu^\lambda \cong {^{\imath}\mathcal{Y}}_{\mu} [\bm z] / \langle \mathsf A_i^{(r)},~\delta_{\bar{\mathbf{v}}_j, \bar 0}\mathsf B_{j}^{(s)} \mid i \in {\mathbb I},j\in{\mathbb I}_0, r > \mathbf{v}_i,s>\mathbf{v}_j \rangle,$$

induced by the epimorphism $\mathsf\Phi_\mu^\lambda$. This would give an explicit presentation of the truncated shifted iYangian by identifying the kernel of the iGKLO homomorphism with the ideal generated by the indicated Cartan and $\mathsf B$-coefficients, extending the analogous presentation for ordinary truncated shifted Yangians; proving the assertion requires establishing that these evident kernel elements generate the full kernel.