Calderón Moreno–Mond–Narváez Macarro–Castro Jiménez conjecture for free divisors

Let $X$ be a complex analytic manifold of dimension $n$, and let $D\subset X$ be a free divisor. Say that $D$ satisfies LCT when the inclusion of logarithmic into meromorphic de Rham complexes is a quasi-isomorphism, and say that $D$ is strongly Euler-homogeneous when it has the corresponding strong Euler-homogeneity property at every point. Calderón Moreno–Mond–Narváez Macarro–Castro Jiménez conjecture. If $D$ satisfies LCT, then $D$ is strongly Euler-homogeneous. The conjecture is proved in several cases in the paper, including ambient dimension at most four, but remains open in general.