Strong Euler homogeneity conjecture for free divisors

Let $D$ be a free divisor. The logarithmic comparison theorem holds for $D$ when the de Rham morphism

$$\Omega_X^\bullet(\log D)\longrightarrow j_*\Omega_U^\bullet\simeq\mathbb{R}j_*\mathbb{C}_U$$

is a quasi-isomorphism, where $j\colon U=X\setminus D\hookrightarrow X$ is the inclusion. Strong Euler homogeneity conjecture. If a free divisor satisfies the logarithmic comparison theorem, then it must be strongly Euler homogeneous. The conjecture is established for Koszul free divisors and for free divisors in dimension at most $3$; its status beyond these cases is not specified here.