  We present a new distance oracle in the fully dynamic setting: given a
weighted undirected graph $G=(V,E)$ with $n$ vertices undergoing both edge
insertions and deletions, and an arbitrary parameter $\epsilon$ where
$\epsilon\in[1/\log^{c} n,1]$ and $c>0$ is a small constant, we can
deterministically maintain a data structure with $n^{\epsilon}$ worst-case
update time that, given any pair of vertices $(u,v)$, returns a $2^{{\rm
poly}(1/\epsilon)}$-approximate distance between $u$ and $v$ in ${\rm
poly}(1/\epsilon)\log\log n$ query time.
  Our algorithm significantly advances the state-of-the-art in two aspects,
both for fully dynamic algorithms and even decremental algorithms. First, no
existing algorithm with worst-case update time guarantees a
$o(n)$-approximation while also achieving an $n^{2-\Omega(1)}$ update and
$n^{o(1)}$ query time, while our algorithm offers a constant
$O_{\epsilon}(1)$-approximation with $n^{\epsilon}$ update time and
$O_{\epsilon}(\log \log n)$ query time. Second, even if amortized update time
is allowed, it is the first deterministic constant-approximation algorithm with
$n^{1-\Omega(1)}$ update and query time. The best result in this direction is
the recent deterministic distance oracle by Chuzhoy and Zhang [STOC 2023] which
achieves an approximation of $(\log\log n)^{2^{O(1/\epsilon^{3})}}$ with
amortized update time of $n^{\epsilon}$ and query time of $2^{{\rm
poly}(1/\epsilon)}\log n\log\log n$.
  We obtain the result by dynamizing tools related to length-constrained
expanders [Haeupler-R\"acke-Ghaffari, STOC 2022; Haeupler-Hershkowitz-Tan,
2023; Haeupler-Huebotter-Ghaffari, 2022]. Our technique completely bypasses the
40-year-old Even-Shiloach tree, which has remained the most pervasive tool in
the area but is inherently amortized.
