Katsumasa–Roff–Yoshinaga conjecture on Hausdorff continuity of magnitude

Yes, with a quantitative bound: magnitude is Hausdorff-continuous at every nonempty finite subset of a finite-dimensional positive definite normed space, with a local Lipschitz-type estimate in the Hausdorff distance whose constants depend on the number of points, the dimension and the least eigenvalue of the similarity matrix, and with compact approximants allowed. The paper also obtains convergence of aggregated weights and a continuity criterion in L_1 by local order oscillation, and, in the other direction, a compact convex subset of L_1[0,1] whose finite subsets approach a singleton with magnitudes tending to 3/2, which refutes an implication stated in Kalisnik and Lesnik's preprint from the one-point property to singleton continuity.

Yes, with a quantitative bound: magnitude is Hausdorff-continuous at every nonempty finite subset of a finite-dimensional positive definite normed space, with a local Lipschitz-type estimate in the Hausdorff distance whose constants depend on the number of points, the dimension and the least eigenvalue of the similarity matrix, and with compact approximants allowed. The paper also obtains convergence of aggregated weights and a continuity criterion in L_1 by local order oscillation, and, in the other direction, a compact convex subset of L_1[0,1] whose finite subsets approach a singleton with magnitudes tending to 3/2, which refutes an implication stated in Kalisnik and Lesnik's preprint from the one-point property to singleton continuity.