The tangent-cone Milnor-fiber conjecture for embedded topologically equivalent hypersurface germs

Let $f,g:(\mathbb{C}^d,0)\rightarrow(\mathbb{C},0)$ be two germs of holomorphic functions. Their initial forms are their lowest-degree nonzero homogeneous parts, and their Milnor fibers are the corresponding Milnor fibers at the origin. Tangent-cone Milnor-fiber conjecture. If $f$ and $g$ are embedded topologically equivalent, then the Milnor fibers of their initial forms are homotopy equivalent. This conjecture concerns Zariski's Problem B and proposes that, despite the tangent cones themselves having different topology in known examples, their Milnor fibers retain the same homotopy type; its general status is not resolved in the source.