Hilbert polynomial conjecture for top Kähler differentials of fat point schemes

Let $K$ be the ground field, let $\mathbb W=m_1P_1+\cdots+m_sP_s$ be a fat point scheme in $\mathbb P^n$, and let

$$\mathbb Y=(m_1-1)P_1+\cdots+(m_s-1)P_s.$$

Write $R_{\mathbb W}$ for the homogeneous coordinate ring of $\mathbb W$, and let $\Omega^{n+1}_{R_{\mathbb W}/K}$ denote its module of Kähler differentials of degree $n+1$. Hilbert polynomial conjecture. One has

$$\operatorname{HP}_{\Omega^{n+1}_{R_{\mathbb W}/K}}(z)=\operatorname{HP}_{\mathbb Y}(z).$$

The formula generalizes the corresponding result for reduced point sets, but the source states that no explicit formula is known in general for the Hilbert polynomial of the top Kähler differentials of a non-reduced fat point scheme. Thus the assertion remains open.