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Suppose a user answers a question in the following manner:

See my paper here: [insert paper reference link here] for your answer. Specifically, look at the theorem (insert theorem number here) which proves that (insert result here).

The post does not show step-by-step, logical argument; it's essentially just a link to a paper that could potentially have the answer to the OP's question.

Is such a post considered "promotional"? I know what some obvious examples of promotional posts are (i.e., links to a website that has nothing to do with the OP) but I'm unsure of examples like this.

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No, if the paper is indeed relevant to the question at hand, this is an appropriate post and should not be flagged as spam.

According to the site rules, it is actually okay to mention your own products in your answers, as long as you disclose your affiliation. In the example you mention, the poster explicitly states that they are the author of the paper in question.

I think it is reasonable to be even more tolerant of people discussing their own papers than commercial products, since they typically do not have a direct financial stake in a paper.

If the reference given is blatantly irrelevant to the question, you could flag as spam. If it's somewhat related and apparently offered in good faith, but is incomplete or actually misses the point of the question, you could leave a comment pointing this out, and downvote if you wish to do so in order to signal the problem to others.

If you don't feel you have the expertise to accurately judge whether the reference is appropriate or not, leave it alone. Someone who does will eventually take a look.

As a separate issue, it would be desirable for the answer to give a summary of what can be found in the referenced paper, in addition to the reference/link itself; this is a general Stack Exchange principle. However, a main part of the rationale for this is to ensure that the answer retains some usefulness if the link goes down. If the reference is to a paper in the archival literature, this should not be a concern. So I would not worry about that issue so much; the answer as it stands is not as good as it could be, but it's okay.

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Take the viewpoint of a person who asked a question, or is interested in knowing the answer. You want to know if some upper bound holds. Someone drops by and says: "This upper bound is in Theorem 5 of my paper". Will you tell them that their remark is ...

... not useful or relevant, but promotional

as in the flag description? I hope not.

This is an answer, albeit a brief one. It contains a stable reference to the literature (journal name and issue, etc), not just a link. So it does not fall under "link-only" answers either.

Incidentally, this is an example of why SE still allows unregistered users to post answers on every site. The author stopped by once and will probably never be seen again. He was never going to write something painfully long, but dropped a nugget of information than nobody else in that thread had. Nice.

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    $\begingroup$ A Good Thing$^\text{tm}$ for the regulars to do, though, would be to look up that paper and copy Theorem 5 into the answer (assuming the paper can be found without violating journal access laws, etc.). $\endgroup$ – apnorton Nov 21 '14 at 4:23
  • $\begingroup$ This might be irrelevant here. Still, this question on SciFi.SE took an unexpected twist when the screenwriter himself (unregistered) came and answered. $\endgroup$ – d80d2729a352b1366139fc119d3345 Nov 21 '14 at 11:45

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