Teissier's conjecture on sectional Milnor numbers and topological type

Let $(X,x)$ and $(Y,y)$ be germs of isolated hypersurface singularities with the same topological type. For a germ $(X,x)$, let $4\mu^{(i)}(X,x)4$ denote its $i$th sectional Milnor number, and write

$$\mu^*(X,x)=(\mu^{(n+1)}(X,x),\mu^{(n)}(X,x),\ldots,\mu^{(0)}(X,x)).$$

Teissier's conjecture. If the germs have the same topological type, then

$$\mu^*(X,x)=\mu^*(Y,y).$$

The conjecture asserts that the full sequence of sectional Milnor numbers is a topological invariant. It contains Zariski's multiplicity conjecture, but was disproved in 1975 by J. Briançon and J.-P. Speder.