Generating-function conjecture for Thom polynomials of nilpotent algebras

Let $Q$ be a $[?]$-dimensional, commutative, nilpotent algebra with $\deg(\operatorname{tp}_Q(l))=\mu\cdot l+\gamma$. Write

$$D_j=\sum_{i=0}^{\infty}\frac{c_i}{z_j^i},\qquad \operatorname{dis}_\mu=\prod_{i=1}^{\mu}\prod_{j=i+1}^{\mu}(z_i-z_j),$$

and let $\operatorname{RES}$ denote the iterated residue in the variables $z_1,\ldots,z_\mu$. Generating-function conjecture. (a) There exists a rational function $k_Q$ in $z_1,\ldots,z_\mu$, of degree $\gamma-\binom{\mu+1}{2}$, such that

$$\operatorname{tp}_Q(l)=\operatorname{RES}\left(k_Q\cdot\operatorname{dis}_\mu\cdot\prod_{i=1}^{\mu}z_i^lD_i\right).$$

(b) The generating function has the form

$$k_Q(z_1,\ldots,z_\mu)=\frac{h(z_1,\ldots,z_\mu)}{\prod_{a\in A}(z_{i_a}+z_{j_a}-z_{s_a})},$$

where $h$ is a polynomial and $\{i_a,j_a,s_a\}_{a\in A}$ is a repetition-free list of indices satisfying $i_a\leq j_a<s_a$ for every $a\in A$. This extends the generating-function theorem of Berczi and Szenes for Morin singularities; the source reports that the conjecture was expected to be proved in work in progress by M. Kazarian.