Sometimes (maybe once a month if it's a busy month) we have a tough question in theoretical science on Computer Science Stack Exchange that nobody can answer.
After a while we tend to presume that if nobody answered, it's because nobody knows, which makes the question research-level. (It's usually clear which questions went unanswered because nobody knows and which questions went unanswered because nobody bothered.)
While research-level questions in theoretical computer science are on-topic on CS.SE, it is better if questions get answered. So if a question was asked on CS.SE but would also be suitable for Theoretical Computer Science, usually someone suggests migrating it there.
Assuming that the question is indeed about theoretical computer science, that it has gone unanswered for long enough that we doubt it will be answered on CS.SE, and that the asker is willing, should we migrate the question to CSTheory.SE? Should we ask first, and where? (Chat? but it's pretty much dead.)
Only moderators of CS.SE can initiate the migration; if we do it it would typically be in response to a flag, often a flag from the asker.
Note that if you feel that a question should not have been migrated to CSTheory, you can close it; this will bounce the question back to its original site, but not reopen it there. (This is known as rejecting the migration.) If you find a question migrated from CS.SE and you think that it is not suitable for CSTheory.SE but should have remained open on CS.SE, please vote to close it here, and once it is closed here please flag it for reopening on CS.SE.