  Designing approximate all-pairs distance oracles in the fully dynamic setting
is one of the central problems in dynamic graph algorithms. Despite extensive
research on this topic, the first result breaking the $O(\sqrt{n})$ barrier on
the update time for any non-trivial approximation was introduced only recently
by Forster, Goranci and Henzinger [SODA'21] who achieved $m^{1/\rho+o(1)}$
amortized update time with a $O(\log n)^{3\rho-2}$ factor in the approximation
ratio, for any parameter $\rho \geq 1$.
  In this paper, we give the first constant-stretch fully dynamic distance
oracle with a small polynomial update and query time. Prior work required
either at least a poly-logarithmic approximation or much larger update time.
Our result gives a more fine-grained trade-off between stretch and update time,
for instance we can achieve constant stretch of $O(\frac{1}{\rho^2})^{4/\rho}$
in amortized update time $\tilde{O}(n^{\rho})$, and query time
$\tilde{O}(n^{\rho/8})$ for a constant parameter $\rho <1$. Our algorithm is
randomized and assumes an oblivious adversary.
  A core technical idea underlying our construction is to design a black-box
reduction from decremental approximate hub-labeling schemes to fully dynamic
distance oracles, which may be of independent interest. We then apply this
reduction repeatedly to an existing decremental algorithm to bootstrap our
fully dynamic solution.
