Degree-Free Spectral Independence for Log-Concave Holant Measures

We establish a degree-independent bound on spectral independence for log-concave Holant problems on simple graphs. As a corollary, we obtain relaxation-time bounds for Glauber dynamics of $O_{\lambda }(m)$ for the monomer-dimer model at activity $\lambda$ and $O_{b,\lambda }(m)$ for $b$-matchings at fugacity $\lambda >0$, where $m$ is the number of edges. For uniform $b$-matchings, the relaxation-time bound improves to $O(bm)$. The main proof ideas were found using GPT-5.6 Sol.