  We provide new query complexity separations against sensitivity for total
Boolean functions: a power $3$ separation between deterministic (and even
randomized or quantum) query complexity and sensitivity, and a power $2.22$
separation between certificate complexity and sensitivity. We get these
separations by using a new connection between sensitivity and a seemingly
unrelated measure called one-sided unambiguous certificate complexity
($UC_{min}$). We also show that $UC_{min}$ is lower-bounded by fractional block
sensitivity, which means we cannot use these techniques to get a
super-quadratic separation between $bs(f)$ and $s(f)$. We also provide a
quadratic separation between the tree-sensitivity and decision tree complexity
of Boolean functions, disproving a conjecture of Gopalan, Servedio, Tal, and
Wigderson (CCC 2016).
  Along the way, we give a power $1.22$ separation between certificate
complexity and one-sided unambiguous certificate complexity, improving the
power $1.128$ separation due to G\"o\"os (FOCS 2015). As a consequence, we
obtain an improved $\Omega(\log^{1.22} n)$ lower-bound on the
co-nondeterministic communication complexity of the Clique vs. Independent Set
problem.
