Hertling's variance conjecture for spectrum numbers

Let $f\in\mathcal O_{n+1}$ be a germ defining an isolated singularity at the origin, with Milnor number $bc$. Let $b1_1\leq\cdots\leq\alpha_bc$ be its spectrum numbers.

Hertling's conjecture. The spectrum numbers satisfy

$$\frac{1}{\mu}\sum_{i=1}^{\mu}\left(\alpha_i-\frac{n+1}{2}\right)^2\leq\frac{\alpha_\mu-\alpha_1}{12}.$$

Hertling proposed this inequality in 2000; it asserts that the variance of the spectrum is at most one twelfth of its range. Its resolution is not specified in the source.