Topological classification conjecture for Poincaré-type foliation germs

Let two holomorphic foliation germs of rank $1$ with isolated singularities at $0\in\mathbb{C}^n$ be of Poincaré type. For each germ, choose a vector field representing it and consider the tuple of eigenvalues of the vector field's linear part. A ray configuration is the ordered partition of the eigenvalues into subsets whose elements lie on the same real ray from the origin, with the subsets ordered by increasing angle from the positive real axis; two ray configurations are equivalent if their partition-subset sizes agree in order, or agree after reversing the order of one partition. For corresponding subsets $\{i_1,\ldots,i_k\}$ and $\{j_1,\ldots,j_k\}$, define

$$L_1=\left\{z_l=0:l\neq i_1,\ldots,i_k\right\},\qquad L_2=\left\{z_m=0:m\neq j_1,\ldots,j_k\right\}\subset\mathbb{C}^n.$$

Topological classification conjecture. The two foliation germs are topologically equivalent if and only if: (1) the ray configurations of their eigenvalue tuples are equivalent; and (2) for every pair of corresponding partition subsets, the restrictions of the two germs to $L_1$ and $L_2$ are holomorphically equivalent.

The conjecture extends the two-dimensional classification to arbitrary dimensions and predicts that the ray configuration, together with the holomorphic equivalence classes of the restrictions associated with its partition subsets, completely determines the topological equivalence class. It also predicts that inessential resonant monomials do not affect that class. The source provides no resolution status.