Weak R-equivalence conjecture for weighted homogeneous polynomials

Let $f,g$ be weighted homogeneous polynomials on $\mathbb{C}^n$ of the same degree $d$, with weight vectors ${\bf w}_f$ and ${\bf w}_g$. Two such polynomials are weakly R-equivalent when the relevant graded linear subspaces of their Milnor algebras are isomorphic. Weak R-equivalence conjecture. If ${\bf w}_f$ and ${\bf w}_g$ coincide up to permutations, then $f$ and $g$ are weakly R-equivalent. The conjecture would imply that the Sasakian Hodge numbers and the natural CN invariant depend only on the weight vector; it is motivated by initial empirical observations and is not resolved in the source.