Stringy invariants and toric Artin stacks

We propose a conjectural framework for computing Gorenstein measures and stringy Hodge numbers in terms of motivic integration over arcs smooth Artin stacks, we verify this the case fantastacks, which are certain toric stacks that provide (non-separated) resolutions singularities varieties. Specifically, let $\mathcal{X}$ be stack admitting good moduli space $\pi: \mathcal{X} \to X$, assume $X$ is variety with log-terminal singularities, $\pi$ induces an isomorphism nonempty open subset $X$, exceptional locus has codimension at least 2. conjecture formula measure function measuring degree to non-separated. also if stabilizers special groups sense Serre, then almost all lift $\mathcal{X}$, explain how case, our conjectures imply integral $\mathcal{X}$. prove these where fantastack.