Equality of discriminant Milnor and Tjurina numbers for matrix families

Let $M:(\mathbb{C}^s,0)\to\operatorname{Mat}_n$ be a germ of any of the three types of matrix families considered in the paper. Assume that the number $s$ of parameters is at least the codimension of the discriminant $\Delta$ in $\operatorname{Mat}_n$, and that the Tjurina number $\tau_{\operatorname{SL},\operatorname{Mat}_n}(M)$ is finite.

Equality conjecture.

$$\mu_\Delta(M)=\tau_{\operatorname{SL},\operatorname{Mat}_n}(M).$$

This predicts that, under the stated parameter and finiteness hypotheses, the Milnor number associated with the discriminant equals the corresponding Tjurina number. The supplied parser gives no evidence resolving the conjecture, so its status remains open.