Hertling's conjecture on TERP structures and eigenvalues of \mathcal{Q}

Let $M$ be the base space of a semiuniversal unfolding $F$ of a singularity, equipped with a \emph{TERP}(n+1)-structure, and let $\mathcal{E}$ denote the Euler vector field. Let $R$ be the set where the \emph{TERP}(n+1)-structure is not a tr\emph{TERP}(n+1)-structure, and define

$$\operatorname{Exp}(F_p):=\bigcup_{x\in\operatorname{Sing}(F_p)}\operatorname{Exp}(F_p,x).$$

Hertling's conjecture. For any $p\in M$, the set $R$ does not contain the $\mathcal{E}+\overline{\mathcal{E}}$ orbit of $p$. Far enough along the flow of $\mathcal{E}+\overline{\mathcal{E}}$, one no longer meets $R$, the Hermitian metric $h$ is positive definite, and the eigenvalues of $\mathcal{Q}$ tend to

$$\operatorname{Exp}(F_p)-\frac{n+1}{2}.$$

This conjecture concerns the asymptotic behavior of TERP structures along the Euler flow and predicts eventual positivity of the Hermitian metric together with a precise limiting spectrum for $\mathcal{Q}$. The source gives no resolution, so its status remains open.