Half-integral-weight modularity conjecture for refined special cycles

Let $(V,Q)=(B^{\operatorname{Tr}=0},D_0\cdot\operatorname{nr})$, let $\varphi$ be a Schwartz function, and let $\{Z(t,\varphi;H)\}$ be the refined cohomological class attached to the special cycle $Z(t,\varphi;H)$. Half-integral-weight modularity conjecture. In this situation, the generating series

$$\sum_{\substack{t\in\mathcal O_F\\ t\gg0}}\{Z(t,\varphi;H)\}q^t$$

is a Hilbert modular form of weight $3/2$.

This predicts a modular generating series for refined special-cycle classes and is intended to support an adaptation of the work of Yuan, Zhang and Zhang; the supplied source gives no resolution.