Hertling's asymptotic conjecture for CDV-structures on singularity unfoldings

Let $M$ be the base space of an unfolding $F$ of a singularity with a CDV-structure, let $R\subset M$ be the real analytic exceptional subvariety, let $E+\overline E$ be the associated real vector field, let $h$ be the hermitian metric, and let $\mathcal Q$ be the CDV endomorphism. For $t\in M$, write $F_t$ for the restriction of the unfolding to $t$, and let $\operatorname{Exp}(F_t)$ denote the set of exponents of its singularities. Asymptotic conjecture. Starting at any $t\in M$ and proceeding sufficiently far along the flow of $E+\overline E$, one does not meet $R$ anymore, the metric $h$ becomes positive definite, and the eigenvalues of $\mathcal Q$ tend to

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

This predicts the asymptotic behavior of the hermitian metric and grading endomorphism under the renormalization-group flow for Frobenius manifolds arising from singularity unfoldings; the source says that a part of the conjecture is proved in the subsequent theorem.