Stacky Batyrev–Manin–Malle conjecture of Ellenberg–Satriano–Zureick-Brown

Let $\mathfrak{X}$ be a “nice” algebraic stack defined over a number field $K$, and let $\mathcal{E}$ be a “nice” vector bundle on $\mathfrak{X}$. Let $H_{\mathfrak{X},\mathcal{E}}$ denote the height associated with $\mathcal{E}$. Stacky Batyrev–Manin–Malle conjecture. There is an open dense substack $\mathcal{U}$ of $\mathfrak{X}$ such that, for all $\varepsilon>0$,

$$\#\{P\in \mathcal{U}(K):H_{\mathfrak{X},\mathcal{E}}(P)\leq B\}=N_{\mathcal{U},\mathcal{E},K,\varepsilon}(B)=O_\varepsilon(B^{a(\mathcal{E})+\varepsilon}),$$

where $a(\mathcal{E})$ is a number depending at most on $\mathcal{E}$. This is a stacky version of height-counting conjectures encompassing weak forms of the Batyrev–Manin and Malle conjectures; its general status is not specified in the source.