(Sorry for not following the suggested format. If this question eventually gets turned into a FAQ, we can clean all this up.)
There is an existing FAQ item tackles many of the same issues as this question, but from another direction - it explains it as a process, rather than a set of triggers: Guidelines for Inadequately Referenced Answers
From that list we can see some of the items in @ChrisW's answer aren't quite that simple.
"No references at all", for example, has a process of requesting references associated with it. A more accurate description is that a question is deleted when:
- No, or inappropriate, references, AND
- a week has gone by since the user/community was asked to fix it OR the user directly refuses to reference it, AND
- it comes to a moderator's attention (including via a flag), OR it is
one of our very, very occasional sweeps of the oldest unreferenced answers
in which we rarely get as far as answers as recent as 12-months-old.
(Putting it this way probably isn't the clearest approach. If this is unclear, and what we already have is unclear, is there a third approach?)
Those guidelines similarly addresses our approach to original research (which, the recent definitional post suggests, subsumes unjustified arithmetic).
"Not answering the question" tends to be flagged - it is a bit like spam. It is just an unwanted answer. (Spam and deliberate vandalism is more likely to result in a permanent ban rather than just deleting the answer with an explanation.)
Repeating an answer is fine - especially if it is better argued and may earn more upvotes.
(I personally prefer to copy-edit someone else's question to make it better, and let them get the rep for the research part. However, I am not in a position of scratching for enough rep to post comments; I am motivated to have trusted users taking on some of the self-policing roles. I can understand someone preferring to earn their own rep with their own answer.)