Holomorphic arithmetic modularity of the arithmetic special-divisor generating series

Assume the condition in ref {asmp1}. Let $\phi\in\overline{\mathcal {S}}\left(\mathbb {V}\right)^{{\widetilde K_\Lambda}}$, and let $g\in G(\mathbb {A})$. The expression $z(g,\phi)_{{\mathfrak e},{\mathfrak a}}^{\overline{\mathcal L}}$ is an element of

$$\mathcal {A}_{\mathrm{hol}}(G,\mathfrak w)\otimes\widehat{\mathrm {Ch}}^{1}_{\overline{\mathcal L},\mathbb C}(\widetilde{\mathcal X}).$$

Modularity conjecture. Under the stated assumption, the arithmetic generating series $z(g,\phi)_{{\mathfrak e},{\mathfrak a}}^{\overline{\mathcal L}}$ is holomorphic and modular, with values in the arithmetic Chow group $\widehat{\mathrm {Ch}}^{1}_{\overline{\mathcal L},\mathbb C}(\widetilde{\mathcal X})$.

This assertion is presented as a conjectural modularity statement for arithmetic special divisors on the unitary Shimura variety. The supplied text does not state whether it is known or resolved.