Acharya–Douglas minimal-distance conjecture for the string Landscape

Let $\mathcal{C}$ be the configuration space of string vacua, and let physically distinct vacua be points of this space. Acharya–Douglas minimal-distance conjecture. There exists a minimal distance $\epsilon$ in $\mathcal{C}$ between physically distinct vacua.

This conjecture supports the proposal that the string Landscape is a discretum rather than an infinite continuous space of vacua, with finiteness results in geometry providing part of the motivation. Its resolution is not established in the supplied source.