The SSM-Thom polynomial conjecture for multisingularities

Assume $l\geq 1$. Let $\mathcal{C}_l$ be the class of maps under consideration, let $\underline{\eta}$ be a T- or S-multisingularity, and let $\operatorname{ssm}(\Sigma^T_{\underline{\eta}}(f))$ and $\operatorname{ssm}(\Sigma^S_{\underline{\eta}}(f))$ denote the corresponding target and source SSM classes. Write $\mathbb{Q}[[\underline{s}]]$ and $\mathbb{Q}[[\underline{c},\underline{s}]]$ for the indicated formal power-series rings. The SSM-Thom polynomial conjecture. For every T-multisingularity $\underline{\eta}$ there exists a power series $\operatorname{Th}^T_{\underline{\eta}}\in\mathbb{Q}[[\underline{s}]]$ such that, for every map $f:M\to N$ in $\mathcal{C}_l$,

$$\operatorname{Th}^T_{\underline{\eta}}(f)=\operatorname{ssm}(\Sigma^T_{\underline{\eta}}(f))\cdot|\operatorname{Aut}(\underline{\eta})|\in\operatorname{H}^\bullet(N).$$

For every S-multisingularity $\underline{\eta}$ there exists a power series $\operatorname{Th}^S_{\underline{\eta}}\in\mathbb{Q}[[\underline{c},\underline{s}]]$ such that, for every such map,

$$\operatorname{Th}^S_{\underline{\eta}}(f)=\operatorname{ssm}(\Sigma^S_{\underline{\eta}}(f))\cdot|\operatorname{Aut}(\underline{\eta})|\in\operatorname{H}^\bullet(M).$$

The conjecture claims that these universal SSM classes are represented by Thom polynomials. The target version was proved according to the source, while the full source version remains open.