Arnold's corank problem: is the Hessian corank of a hypersurface singularity an ambient topological invariant?

The weighted homogeneous germs $f_1,f_2$ on $\mathbb{C}^N$ ($N>3$, divisible by eight) of the Zariski counterexample are ambiently homeomorphic, have isolated critical points and real coefficients, and have Hessian ranks $16E>0$ and $0$, so their coranks differ. Corank parity is preserved, as Sampaio's theorem requires. Nothing is said about corank in three variables (where it is invariant) or about a minimal dimension.

The weighted homogeneous germs $f_1,f_2$ on $\mathbb{C}^N$ ($N>3$, divisible by eight) of the Zariski counterexample are ambiently homeomorphic, have isolated critical points and real coefficients, and have Hessian ranks $16E>0$ and $0$, so their coranks differ. Corank parity is preserved, as Sampaio's theorem requires. Nothing is said about corank in three variables (where it is invariant) or about a minimal dimension.