Minimality of the Tetrakis generating set for the HTMC–Hölder ball

Determine whether the set of Tetrakis functions introduced in Section 4 provides the smallest (in an appropriate convex-hull sense) generating family for the HTMC unit ball intersected with the Hölder ball, or otherwise characterize a minimal such set.

Background

The authors construct Tetrakis functions as a countable family that approximates the extreme structure of the HTMC ball and show inclusion relations suggesting these functions are near-vertices. However, they do not establish minimality of this family as a generating set. Proving minimality (or identifying a smaller set) would clarify the convex geometry of the HTMC ball and could enable more efficient convex optimization schemes (e.g., Frank–Wolfe) over a reduced dictionary.