Establish the Lagrange-spectrum results for norms beyond the Euclidean norm

Establish whether the theorem on the distribution of points near the origin in the d-dimensional Lagrange spectrum remains valid for norms other than the Euclidean norm, with appropriately modified parameter bounds.

Background

The main theorem is proved using Euclidean balls and Euclidean geometric arguments, particularly in the construction and analysis of target surfaces. The paper observes that analogous results should plausibly hold for other norms, while noting that the cited prior results already apply to arbitrary norms. This is presented as an unresolved extension rather than as a result established in the paper.