Wall-crossing conjecture for self-dual Donaldson--Thomas invariants

Let $(Q,W)$ be a self-dual quiver with potential, and let $\tau$ and $\widetilde{\tau}$ be self-dual weak stability conditions on the associated self-dual abelian category. Let $\mathrm{DT}^{\mathrm{sd}}_\theta(\tau)$ denote the self-dual Donaldson--Thomas invariants, and let $\bar{\chi}$, $\widetilde{\chi}$, $\bar{\chi}^{\mathrm{sd}}$, and $\widetilde{\chi}^{\mathrm{sd}}$ denote the ordinary and self-dual Euler-form coefficients. Wall-crossing conjecture for self-dual Donaldson--Thomas invariants. For any two self-dual weak stability conditions, the invariants $\mathrm{DT}^{\mathrm{sd}}_\theta(\tau)$ satisfy the wall-crossing formula referenced in the source, with coefficients $\bar{\chi}({\cdots})$, $\widetilde{\chi}({\cdots})$, $\bar{\chi}^{\mathrm{sd}}({\cdots})$, and $\widetilde{\chi}^{\mathrm{sd}}({\cdots})$ given by the corresponding coefficients for $Q$ regarded as a self-dual quiver without relations. The conjecture seeks the self-dual analogue of the established ordinary Donaldson--Thomas wall-crossing formula; no resolution is supplied in the source.