The primary-component masslessness conjecture for the structure sheaf

Let $X$ be a Calabi–Yau threefold, and let $\Delta$ be the discriminant locus in the moduli space of conformal field theories. Its primary component is the component corresponding to viewing the full convex hull of the monomial set as a face of itself. Let $\mathcal{O}_X$ be the structure sheaf, and consider the 6-brane associated with it and its translates. Primary-component masslessness conjecture. At any point on the primary component of $\Delta$ reached by a suitable path from a suitable basepoint, the 6-brane associated with $\mathcal{O}_X$ and its translates should become massless; at a generic point, no other D-branes should become massless. This conjecture identifies the primary discriminant component with the locus where the structure-sheaf brane becomes massless; the source gives no resolution.