The universal-invariant conjecture for coherent sheaves on Calabi–Yau fourfolds

Let $X$ be a Calabi–Yau $4$-fold and let $\mathcal A=\operatorname{Coh}(X)$, with the moduli, stability, orientation, homology, and virtual-class data specified in the universal enumerative-invariant assumptions. Universal-invariant conjecture for Calabi–Yau fourfolds. The universal-invariant conjecture holds for $\mathcal A=\operatorname{Coh}(X)$ when $X$ is a Calabi–Yau $4$-fold. This would extend universal rational-homology invariants and wall-crossing formulas to the Calabi–Yau fourfold setting, using Borisov–Joyce or Oh–Thomas virtual classes and chosen orientations. The required orientation and virtual-class technology is available in important cases, but the full universal package remains conjectural.