Uniqueness of convex hull layering in 6-hole-free 29-point sets

Determine whether every 29-point planar set in general position that contains no empty convex hexagon has the same convex hull layer-size sequence as the known Overmars example, namely layers of sizes (3, 4, 7, 7, 7, 1).

Background

Overmars constructed a 29-point set with no 6-hole whose convex hull layers have sizes (3, 4, 7, 7, 7, 1). Using their SAT-based analysis, the authors found that all 6-hole-free 29-point sets they examined share structural constraints (e.g., exactly three points on the outer hull and at least four on the next layer).

They suspect, but have not verified, that all 6-hole-free 29-point sets exhibit exactly the same convex hull layer structure as Overmars’ example, which would impose a strong classification of such extremal configurations.