HasDSDimLE.hasNatarajanDimLE has no converse. The six-cycle on a two-point domain has Natarajan dimension 1, a Natarajan witness on both points being a four-cycle, while its whole trace family is a two-dimensional pseudo-cube, so its DS dimension is at least 2.

This is the hexagon Brukhim, Carmon, Dinur, Moran and Yehudayoff record after their Definition 6, and the four-cycle test the proof turns on is their Example 7. Their Theorem 2 pushes the separation to a class of Natarajan dimension 1 and infinite DS dimension; that construction rests on hyperbolic pseudo-manifolds and is cited in the module docstring rather than formalised here.