Third-stage Euclidean minimum lower bound

Determine whether the lower-bound statement that $b\in E'_k$ implies $M^k(f)\ge 1/f(b)$ remains valid for $k=3$.

Background

The paper establishes the bound for $k=1$ and $k=2$ using the sets $E'_k$ and then observes that the same formulation would give a lower bound for higher-stage Euclidean minima. The authors explicitly indicate uncertainty already at the third stage, so this is an unresolved extension of their method.