The canonical oriented d-critical structure conjecture for stable pair moduli

Let $P_n(X,\beta)$ be the moduli space of Pandharipande–Thomas stable pairs. A perverse sheaf on this moduli space is denoted by $\phi_{n,\beta}$, and set

$$\Phi_{n,\beta}=\phi_{n,\beta}[-\dim(P_n(X,\beta))].$$

Canonical oriented d-critical structure conjecture. There exists a canonical oriented d-critical locus structure on $P_n(X,\beta)$ inducing $\phi_{n,\beta}$, with $\Phi_{n,\beta}=\mathbb{Q}$ whenever $P_n(X,\beta)$ is smooth.

The conjecture is needed to define refined stable pair invariants from perverse sheaves. The source notes that canonical orientation results for moduli spaces of sheaves on Calabi–Yau threefolds provide evidence, but gives no resolution for stable pair moduli.