Borisov–Oblomkov–Pandharipande–Yin conjecture for Donaldson–Thomas invariants of abelian threefolds

Let $(A,H)$ be a principally polarized abelian threefold with Picard rank $\rho(A)=1$. For nonzero $(\beta,n)\in\mathbb{Z}^2$, define $\operatorname{DT}_{\beta,n}=\operatorname{DT}_H(1,0,-\beta,-n)$, and let $\mathsf{a}(n)$ and $\mathsf{n}(\beta,k)$ be defined by the Fourier expansion and divisor sum described in the setup. Borisov–Oblomkov–Pandharipande–Yin conjecture. Assuming $\beta>0$, or $\beta=0$ and $n>0$, one has

$$\operatorname{DT}_{\beta,n}=(-1)^n\sum_{\substack{k\geq 1\\ k\mid n}}\frac{1}{k}\mathsf{n}(\beta,k)\mathsf{a}\left(\frac{4\beta^3-n^2}{k^2}\right).$$

This conjectural formula gives the predicted curve-counting invariants for principally polarized abelian threefolds of Picard rank one; the source presents it as a conjecture proposed in the cited work, with no resolution supplied here.