A 0.41275 lower bound for the three-dimensional Blaschke-Lebesgue problem

We prove that every convex body $K\subset\mathbb{R}^3$ of constant width $w>0$ satisfies \[ \operatorname{Vol}(K)\ge \frac{1651}{4000}w^3=0.41275\,w^3. \] This improves the certified lower bound $0.411040473721188\ldots\,w^3$ announced by Hyra and the earlier spectral bound $4πw^3/33$ of Nishioka.