Calderón-Moreno et al.'s conjecture that LCT implies strong Euler homogeneity for free divisors

Let $D$ be a free divisor, and suppose that the logarithmic comparison theorem (LCT) holds for $D$, meaning that the inclusion

$$\Omega_V^\bullet(\log D)\hookrightarrow\Omega_V^\bullet(*D)$$

is a quasi-isomorphism. A free divisor is strongly Euler homogeneous if, at every point of $D$, there is a local Euler vector field for a local defining equation of $D$ that vanishes at that point. Calderón-Moreno et al.'s conjecture. LCT implies strong Euler homogeneity for $D$. The conjecture concerns the relationship between the logarithmic comparison theorem and Euler homogeneity for free divisors. It was proved for $n\leq 3$, while the general case is not resolved in the supplied source.