Equivalence of Milnor-Hamm tube and sphere fibrations

Let $G:({\mathbb R}^{m},0)\to({\mathbb R}^{p},0)$ be a nice analytic map germ with $m>p\geq2$ and radial discriminant, and suppose that $\Psi_G$ is $\rho$-regular. Assume that the Milnor-Hamm tube fibration and the Milnor-Hamm sphere fibration both exist. Equivalence conjecture. The Milnor-Hamm tube fibration and the Milnor-Hamm sphere fibration are equivalent. The equivalence problem concerns whether the two fibrations can be related under these hypotheses; the preceding theorem establishes this when a Milnor vector field exists, while the source notes that existence of such a field is not known without additional conditions, even when ${\rm Sing}\,G=\{0\}$.