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I received a paper for review from MathReviews (so, not an actual peer review).

It is from a journal with Q2 classification according to Scimago, so I expect it to not be a predatory journal, although the statistics show a decline over time of the journal.

The title of the paper caught my attention, as it talks about a result on a well-known operator R in my community, but once inside the paper, the author goes on and defines R with the definition of another well-known operator H. The author even gives references for such a definition (citing previous classical work) and these references clearly state that the operator is named as H, not R.

Ok, I thought it could be just a naming mistake, that shouldn't change the actual results (it would just make the paper uncitable, as no one looking for results for H would find this one that calls it R).

Afterward, I checked the next definition, but it is written in a mathematically wrong fashion (basically, it makes no sense).

Then I go to the first paragraph in the introduction and check the first 3 references, typically these are to justify why it is relevant to study the subject of the paper. These 3 references are completely unrelated neither to operator H or R and don't correspond to what the author describes them to be.

So for me, it is clear this is a fake paper (I think I would call it like that, I don't have a proper name for this).

What to do now?

I first thought to just review accordingly in MathReviews (i.e. estate that the paper is a fake one), but now I'm wondering if I should go straight to the Journal's chief editor to denounce this. I cannot even fathom how such a paper even passed through peer review.

This question is related to the one in here What should I do when images in a publication appear to have been faked? Albeit, I feel that in this case there is nothing to discuss with the author. Furthermore, given the (possibly intentional) operator naming mistake, this paper most likely won't ever be cited by anyone... not at least someone writing real work; therefore, it wouldn't have the negative impact of a scientific paper from some reputable institution or scientists that employs fake data.


Just as an addition:

I skimmed through some of the cited papers, and they give me also the impression to be rambling nonsense (and they are published in the same journal). I have not actually deeply scrutinized them (takes time), but I'm starting to get the impression this could be something "bigger". I've tried to google this author and I cannot find him, similarly, I tried to look for one of the sketchy authors that was cited several times and I also cannot find him; my best guess is that probably they have a personal webpage in a foreign language.

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    What kind of a review are you doing on this paper, if not a peer review? – David Z Dec 20 '18 at 23:17
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    I may be biased, but this is exactly the situation for an Exceptional MathReview :) – Kimball Dec 21 '18 at 2:25
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    @DavidZ: MathReviews and zbMath publish a short summary of almost every math paper published as part of their bibliographic database of math papers. These are post-publication. – Alexander Woo Dec 21 '18 at 6:07
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    When/if you find out more, could you please come back and tell us about is? – Ivana Dec 21 '18 at 15:15
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    Have the cited papers already been reviewed in Math Reviews? If so, what did the reviewers say about them? – Andreas Blass Dec 22 '18 at 1:13
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The first thing to do is to contact the editor at math reviews and express your doubts about the paper without making accusations of impropriety. Describe what you have found using neutral language. Suggest that others be enlisted to check further into the provenance and accuracy of the paper.

If you are in your early career, it is especially important not to assert misconduct.

You could also contact the editor of the journal in which the paper was published, saying you have serious doubts about the validity of the paper and, perhaps, that you aren't able to follow the citations.

It is hopefully enough to shake the tree and wait to see what falls out. But do it in such a way that you can't be retaliated against, unless you have enough reputation to sustain you.

Of course, it goes without saying that you need to be clear in your objections and to have carefully considered alternative explanations.

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