Expected boundary vanishings for rank-zero Donaldson–Thomas invariants on the quintic

Let $X_5$ be the quintic threefold, let $H$ be its hyperplane class, and set $\kappa=H^3=5$. Write $\overline{\Omega}_H$ for the rank-zero invariant with Chern-character arguments displayed below. Expected quintic boundary vanishings. The following vanishings are expected:

$$\overline{\Omega}_H\left(0,H,\pm\left(\frac12+\frac1\kappa\right)H^2,\frac{H^3}{6}\right)=0,$$

and

$$\overline{\Omega}_H\left(0,H,\pm\left(\frac12+\frac2\kappa\right)H^2,\left(-\frac{m}{\kappa}+\frac16\right)H^3\right)=0\qquad\text{for }m=0,-1.$$

These predictions concern stable-pair and rank-zero Donaldson–Thomas invariants near the Castelnuovo bound and are motivated in the source by physical arguments. No resolution status is given for these expected vanishings.