Conjecture on generic continuity of magnitude for finite subsets of positive definite normed spaces

Let $U$ be a finite-dimensional, positive definite normed space. For a finite subset $X\subseteq U$, write $|X|$ for its magnitude, and equip the set of finite subsets of $U$ with the Hausdorff topology. Magnitude continuity conjecture. The function

$$X\mapsto |X|$$

is continuous with respect to the Hausdorff topology on the set of finite subsets of $U$. In particular, magnitude is stable for finite subsets of Euclidean or taxicab space.

Magnitude is known to be lower semicontinuous on the Gromov–Hausdorff space of compact positive definite metric spaces, and continuous on compact convex subsets of finite-dimensional positive definite normed spaces. The conjecture asks for continuity on all finite subsets, including those in Euclidean and taxicab spaces.