The neutral-hypermultiplet conjecture for frozen F-theory compactifications

Consider a six-dimensional F-theory compactification with a frozen $7$-brane localized along a divisor $D$ and residual discriminant $\widetilde{\Delta}$. Neutral-hypermultiplet conjecture. There exist at least

$$\frac{1}{2}D\cdot\widetilde{\Delta}$$

localized neutral hypermultiplets. This conjecture is motivated by compact frozen F-theory examples and gravitational anomaly cancellation; the proposed lower bound and its interpretation in terms of a weakly coupled type IIB limit remain to be established in general.