Iritani's integral crepant resolution conjecture

Let $\mathcal{X}$ be an orbifold with coarse moduli space $X$, and let $\phi\colon Z\to X$ be a crepant resolution. Iritani's conjecture. There exists an isomorphism

$$\mathbb{U}_{K}\colon K_c(Z)\longrightarrow K_c(\mathcal{X})$$

induced by a Fourier--Mukai equivalence. After analytic continuation, there exists an affine change of flat coordinates $\mathbb{U}_{\rm coh}$ such that: the quantum $\mathcal{D}$-modules of $Z$ and $\mathcal{X}$ are isomorphic in a way preserving their $\widehat{\Gamma}$-integral structures and induced by $\mathbb{U}_{K}$; $\mathbb{U}_{\rm coh}$ identifies the corresponding quantum products; and, for every $V\in K_c(Z)$,

$$\mathcal{F}_Z(V)(\tau)=\pm\,\mathcal{F}_{\mathcal{X}}\bigl(\mathbb{U}_{K}(V)\bigr)\bigl(\mathbb{U}_{\rm coh}(\tau)\bigr),$$

where the sign is independent of $V$. This strengthens the crepant resolution comparison by requiring compatibility with Fourier--Mukai transforms, quantum $\mathcal{D}$-modules, $\widehat{\Gamma}$-integral structures, quantum products, and integral central charges; it is presented as a conjectural framework rather than a result proved in the paper.