The Euler-characteristic discrepancy conjecture for degeneracy-locus Hilbert squares

Let $m\geq1$, let $s\in\{m+3,\ldots,2m+3\}$, and set $n=2s-2m-3$. Let $\mathsf{M}_{m,s}$ be the degeneracy locus considered in the paper and let $Z_{n,s,m}$ be the associated variety. Euler-characteristic discrepancy conjecture. One has

$$e_{\mathrm{top}}(\operatorname{Hilb}^2(\mathsf{M}_{m,s}))-e_{\mathrm{top}}(Z_{n,s,m})=(-1)^{\dim(\mathsf{M}_{m,s})}\frac{1}{s}\binom{2s-m-2}{s-1}\binom{2s-m-3}{s-1}.$$

The formula is motivated by explicit examples, where the discrepancy equals the number of contracted special fibres; its validity in the stated parameter range remains open.