Steenbrink's spectrum conjecture for curve singular loci

Let $f:X\to\mathbf A^1$ be a function on a smooth complex algebraic variety, and let $x$ be a closed point of $f^{-1}(0)$. Suppose the singular locus of $f$ is a curve with local components $\Gamma_\ell$, $1\leq\ell\leq r$, near $x$, and let $m_\ell$ be the multiplicity of $\Gamma_\ell$. For a generic linear form $g$ vanishing at $x$ and $N$ sufficiently large, $f+g^N$ has an isolated singularity at $x$. Let $\alpha_{\ell,j}$ be the exponents of the corresponding family of isolated hypersurface singularities along $\Gamma_\ell\setminus\{x\}$, and let $\beta_{\ell,j}\in[0,1)$ be determined by the eigenvalues $\exp(2\pi i\beta_{\ell,j})$ of the monodromy along that component. Denote by $\operatorname{Sp}(f,x)$ the spectrum of $f$ at $x$. Steenbrink's conjecture. For $N\gg0$,

$$\operatorname{Sp}(f+g^N,x)-\operatorname{Sp}(f,x)=\sum_{\ell,j}t^{\alpha_{\ell,j}+\left(\beta_{\ell,j}/m_\ell N\right)}\frac{1-t}{1-t^{1/m_\ell N}}.$$

The conjecture gives a formula relating the spectrum after a high-power generic perturbation to the spectrum of the original function and the monodromy data along the one-dimensional singular locus. It has been proved by Morihiko Saito using the theory of mixed Hodge modules.