Deformation invariance of numeric orthosymplectic DT invariants on Calabi–Yau threefolds

Prove that the numeric self-dual Donaldson–Thomas invariants $\mathrm{DT}^{\mathrm{sd}}_{\theta}(\tau)$ for Calabi–Yau threefolds are invariant under deformations of the complex structure of the threefold, analogously to the deformation-invariance result for Joyce–Song DT invariants in the linear setting.

Background

The authors introduce orthosymplectic (self-dual) DT invariants for Calabi–Yau threefolds, generalizing classical DT theory beyond the linear case. In the linear case, numerical DT invariants are known to be deformation invariant.

They conjecture an analogous property for the self-dual invariants but explicitly state that they are currently unable to prove it, noting obstacles in adapting existing techniques (e.g., Joyce–Song pairs) to the self-dual setting.