Bi-Lipschitz multiplicity conjecture for complex analytic germs

Let $X\subset \mathbb{C}^n$ and $Y\subset \mathbb{C}^m$ be complex analytic sets with $\dim X=\dim Y=d$. Their germs at zero are bi-Lipschitz homeomorphic if there is a bi-Lipschitz homeomorphism between them. Bi-Lipschitz multiplicity conjecture. If the germs of $X$ and $Y$ at zero are bi-Lipschitz homeomorphic, then their multiplicities satisfy

$$m(X,0)=m(Y,0).$$

This conjecture concerns whether multiplicity is preserved by bi-Lipschitz equivalence of complex analytic germs. The source states that it was proposed in earlier work and that Zariski's broader multiplicity conjecture remains open.