Ding–Hu, Section V, p. 8 (arXiv:1909.11256v3): negative answers to the two open finite-cover questions

We answer negatively both open questions in Ding and Hu, Masking quantum information on hyperdisks, Section V, p. 8, arXiv:1909.11256v3 (15 October 2020): the finite-cover questions for regular subsets of hyperdisks and for nondegenerate masking machines. An explicit four-coordinate example has span dimension three and requires continuum many contained hyperdisks, each a single ray. The same support obstruction gives a complete maskable set requiring continuum many hyperdisks for every prescribed nondegenerate marginal spectrum of rank d >= 4, at every input dimension 3 <= n < d. We also determine the cover cardinalities of the two degenerate examples in the posing paper and distinguish maximal maskable sets of density matrices from convex hulls of phase states.