Split exactness conjecture for maximal compact multigerm equivalence groups

Let $f$ be a finitely $\mathcal{A}$-determined multigerm which is also a critical normalization. Write $D(f)=f(\Sigma(f))$ for its discriminant, and let $\tilde{\operatorname{Inv}}(D(f))$ denote the group of target diffeomorphisms preserving $D(f)$. Let $MC(\mathcal{A}_f)$ and $MC(\mathscr{R}_f)$ denote maximal compact subgroups of the corresponding equivalence groups. Split exactness conjecture. The group $\tilde{\operatorname{Inv}}(D(f))$ admits a maximal compact subgroup $G$, unique up to conjugation, and the sequence

$$0 \to MC(\mathscr{R}_f) \stackrel{i}{\to} MC(\mathcal{A}_f) \stackrel{p}{\to} G \to 0$$

is split exact, so that

$$MC(\mathcal{A}_f)=MC(\mathscr{R}_f)\oplus G.$$

This generalizes the corresponding claim of du Plessis and Wilson from monogerms to multigerms. The source presents it as the goal of the paper, and no resolution is supplied here.