A Near-Quartic Separation Between Certificate Complexity and Quantum Query Complexity

We construct a total Boolean function $f$ for which $Q(f)=\tilde{O}(\sqrt[4]{C(f)})$, where $Q(f)$ denotes the bounded-error quantum query complexity and $C(f)$ denotes the certificate complexity. This resolves a longstanding open question and is tight up to logarithmic factors.