I reproduce further the message sent by a journal, 15 months after the submission. The message contains comments made by anonymous referees.

Let me stress that:

- I trust the journal, otherwise why submitting to it?
- this is the result of the anonymous peer-review after they sit on the paper for 15 months,
- I suppose that the extracts from the reports, provided to me by the managing editor, are the most significant ones, otherwise the message makes no sense,
- the message is reproduced as it is, with the exceptions of links, added by me, the numbering of the referees’ comments and very few comments of my own, [between brackets], where I really could not stop myself.
~~I removed the names of the managing editor and journal, in order to present the comments in a more objective light.~~in fact, there are no reasons to protect maybe the most sloppy peer-review report obtained in the most ridiculous amount of time. The journal is Geometry and Topology. The referees were anonymous, so they could pretend they read the article (but see referee’s comments (3), (6) and (7) which are evidence that at least one of them did not bother to read it in FIFTEEN MONTHS). As for the reason of rejection, because what is written in the reports cannot be one, rationally, I can only speculate.**UPDATE:**

The achieved effect is to keep this paper out of publishing for a year and a half. This article was written in 2009 and it has been previously submitted to:

- Commentationes Mathematicae Universitatis Carolinae (july 2009), retired from CMUC (april 2010), after no referee report in sight; the reply of the editor was: “I am sorry for the long time you had to wait, and I understand your decision. I informed already our referee (who appologizes as well, but points out that your paper is very difficult to read and check)”
- Groups, Geometry and Dynamics, (april 2010), received the following answer (august 2010): “I am sorry for such a late answer, but after consulting with referees and other editors, we arrived to the conclusion that your paper does not fit the scope of our journal.”
- Electronic journal of Combinatorics (january 2011), answered (january 2011): “I have looked at your paper in the arXiv. It’s really outside the scope of E-JC. You need to send it to one of the journals mentioned in your reference list or some other geometric/algebraic journal.”
- Constructive Approximation (nov. 2011), received answer (nov. 2011): “I had an editor quickly look over your manuscript. He suggested that the article is more appropriate for a journal that publishes papers in algebra and geometry. Here is the response we received from the editor: —————- The paper is interesting. It studies the relationship between algebraic and differential structure on manifolds with sub-Riemannian geometry, in particular, Carnot-Caratheodori metric. Such questions are natural in the framework of rigidity theory. I do not know why he submitted the paper to CA. It should be sent to a journal that publishes papers in algebra and geometry. It can be a general journal (like Journal of LMS) or a more specialized journal like “Geometry and Topology” or IJAC (“International Journal of Algebra and Computation”). —————-“
- Geometry and Topology (2 dec. 2011),answered (11 march 2013), see further.

The article just not fits in a place.

_____________________________

Here is the message from the managing editor of Geometry and Topology:

“Dear Prof. Buliga,

I regret to inform you that your paper

has been rejected by G&T . I attach an extract from the referee’s report. Your paper was sent to two referees, and their conclusion was that the though the results are interesting he paper cannot be published in the current form. The referees’ reports are addressed to the editors, so I only give you at the end of this message some extracts from both reports. The editors would be willing to consider your paper again if it is appropriately rewritten.

On behalf of the editorial board I would like to thank you for giving us the opportunity to consider this paper for G&T.

Sincerely

Yasha Eliashberg , Managing Editor of Geometry & Topology

Selected comments from the referees:

(1) I find the paper a bit confusing. the comments give the impression that the theory encompasses manifolds (and sub-Riemannian manifolds), but, if I am not misled, the results only concern groups. I find the quandle characterization of Carnot groups striking. but the paper needs rewriting.

(2) The second paragraph of the abstract should say “… are related to racks and quandles…” Quotes in TeX should be of the form “this phrase is in quotations.” Many people make that mistake — it is an annoying feature of TeX, but I find it off-putting when and author does not fix this. The second item on page 2 the word should be: information line -14 page 2 “obtain” should be “obtained.”

(3) The paper starts Introduction, Outline, Motivation and I still don’t know what the author wants to achieve. I am not an expert here, but I still want some ideas. What, for example is a Carnot group?

[So, there are 3 sections of the article full of explanations of the ideas, but not enough. Moreover, Carnot groups are defined in Definition 4.6 in the article. Even without reading the article, as this referee, one can still find what a Carnot group is, for example by using google, or a trip to the library]

(4) newtheorem environments default to italics. 3.1,3.2 etc should be set in roman font.

(5) After definition 3.3, example 4.1 should be given. Also, delta should be exemplified. Here there is something very interesting from the point of view of quandles: delta is NOT necessarily an automorphism. The reader needs examples to continue.

(6) On page 6 above Remark 3.4, I don’t see the definitions for the original circle operations.

[They are in Definition 3.3, exactly where the referee does not see them.]

I can’t think of a scenario in which )this( is a meaningful grouping. There are several grouping operations provided in TeX; please use one.

At (a), (b), and (c) I got lost in the notation.

… It took me some time to see that the advantage is the statement of Prop.3.5 and the remarks that follow. [Thank you!]

(7) I think that the point of the paper is the paragraph on page 10 above Def. 4.6. I would like to see some more exposition about this early.

[Section 2 “Motivation” is dedicated to this.]

8) What is in the definition 4.6? In 5.3, do X and Y have the same first operation? Why not an empty diamond or filled one for Y?

(9) My overall impression is that the author has a very nice big idea: geometry and algebraic structures emerge togther in a manifold situation. He is arguing that irqs and/or symmetric spaces give rise to tangent-like structures. But I would really like a careful exposition with detailed examples written for a less selected audience.”

_______________________

* UPDATE 2:* I submitted the article to another journal. I hope it is clear that what I am after is fair, rock-solid peer review, which I could learn from and which could improve the article. It is obvious that I think the emergent algebra idea is gorgeous, as the author of it I naturally support it, but not to the point of not accepting critics. But they have to be real critics, with substance and then I welcome them and follow them. That is why I submitted the same file, the one available from arXiv; that is already version 3 and previous versions do not differ much. If I change it then I have to produce a new version, but the substance of the article is well enough (according to my powers) communicated, but not really understood by any of the referees until now. It can be improved, even enormously, and I shall do it eventually, but for the moment, this is really not worthy if the referees are put off by the use of ” or by “obtain -obtained” matters. Maybe I am wrong, surely I am wrong in this respect, but also my past experience tells me that it does not matter how well I present a new idea if the referees don’t really read the paper. This is not meaning I encourage sloppy articles, if you read it then you will see that the paper is densely and carefully written, maybe even too optimized, as the referee’s comment (6) shows. But hey, we are in the internet age, there is no reason anymore to present things as if they are designed to be read in front of a (bored) audience. We have google, we are multitasking, we use hypertext.

E-JC seems to have an automatic response to some articles. And their referees read them rather quickly!

Yes, they gave a timely, honest response. So did Constructive Approximation. Why keep the paper for so long, only to give after a year some inept comments about the latex use of ” and such?

By the way, may I suggest you to split your Definition 3.3 in two parts, to improve readability? 😀

Thanks! Btw I welcome any comments on the paper. There are several articles already on emergent algebras, written after this first one here, or see the series on this blog on the origins of emergent algebras parts (I), (II) , (III).

This leads eventually to graphic lambda calculus, one of the main subjects on this blog.

This is disgraceful. I am so sorry that you have had to waste so much time and effort on this, and for that matter that the time and effort of so many editors and reviewers has also been wasted. What a sensationally stupid system we put up with.

Thanks for passing by. I put a link to your excellent post about not playing the game in the other post on multiple peer-reviews. Looking with envy at the more advanced publishing alternatives in sciences, I still look forward for a system of open, perpetually updating peer-review.

Meanwhile, a bit of laugh is a good medicine.

My impression is that, on a quick scan, an average mathematician can’t understand that. Isn’t it useful to know? as he says it’s a creative idea (and you hadn’t heard of Carnot groups either) — so the exposition of the unusual or unexpected takes extra skill, and you said you don’t like to waste time on exposition.

Haven’t read the paper, just judging based on these blogposts.

Yes, I don’t say that the article is easy to understand, but why pretending one does a review in 15 months? At least, after such a big time I expect to see a review which is useful, like one which finds faults in the reasoning, suggests alternative better views, points to facts unknown to the author. Not one which could be (and probably was) done in 2h, betraying that the referees have not read the paper even once. I have nothing against harsh reviews, actually I welcome any useful comment, be it positive or negative. This is the only thing a journal or publisher may offer today: (well done) peer review. Because the article is published and disseminated since 2009.

Ya. It seems like the referee was too busy / didn’t care. I hear this from many academics, they have too much to do and need to calculate what’s best for their careers.