Contractible stable perturbation conjecture for finitely determined germs

Let $f:(\mathbb{C}^n,0)\to(\mathbb{C}^p,0)$ be an unstable $\mathscr{A}$-finite germ with $n<p$, and let $f_s$ be a stable perturbation. Write $\operatorname{im} f_s$ for the image of the stable perturbation, and let $\mathbb{Z}^+$ denote the positive integers.

Contractible stable perturbation conjecture. There are such germs for which

$$\operatorname{im} f_s\simeq\left\{*\right\}$$

if and only if

$$\frac{p}{p-n}\notin\mathbb{Z}^+.$$

This conjecture proposes a dimension-theoretic characterization of when unstable finitely determined germs can have contractible stable perturbation images. Its resolution status is not specified in the source excerpt.