  Mean-based reconstruction is a fundamental, natural approach to worst-case
trace reconstruction over channels with synchronization errors. It is known
that $\exp(O(n^{1/3}))$ traces are necessary and sufficient for mean-based
worst-case trace reconstruction over the deletion channel, and this result was
also extended to certain channels combining deletions and geometric insertions
of uniformly random bits. In this work, we use a simple extension of the
original complex-analytic approach to show that these results are examples of a
much more general phenomenon. We introduce oblivious synchronization channels,
which map each input bit to an arbitrarily distributed sequence of replications
and insertions of random bits. This general class captures all previously
considered synchronization channels. We show that for any oblivious
synchronization channel whose output length follows a sub-exponential
distribution either mean-based trace reconstruction is impossible or
$\exp(O(n^{1/3}))$ traces suffice for this task.
