Achieve equality Lrad(E) = X in the Fσ case

Construct, for every non-empty Fσ set X ⊂ S^{n−1}, a discrete set E ⊂ D^{n} that is separated and well-approximated such that the radial limit set equals X (i.e., Lrad(E) = X), thereby improving Theorem 3.7 which currently ensures only Lrad(E) ⊇ X.

Background

Theorem 3.7 extends the dimension characterisation to Fσ sets X by showing dim_H(X) equals the minimum critical exponent among separated and well-approximated E with Lrad(E) ⊇ X. The construction uses disjoint scale windows to ensure separation but stops short of equality.

The authors explicitly note the desirability of strengthening Lrad(E) ⊇ X to exact equality Lrad(E) = X in the Fσ setting and state they do not know how to do this.