Alternating-sign conjecture for SSM-Thom polynomials at relative dimension zero

Let $T^{\mathrm{SSM}}(\tau,\ell)$ denote an SSM-Thom polynomial of a singularity $\tau$ and relative dimension $\ell$. For $\ell=0$, the SSM-Thom polynomials have alternating signs in both their Schur and Schur-tilde expansions. The conjecture is motivated by a large number of initial sums of SSM-Thom polynomials calculated by the authors. Its resolution is not specified in the source.