Since the question has gained some attention, I would like to mention here why I have deleted my question titled "Supposed errors in Rosenberg’s proof of the Reconstruction Theorem".

a) I continue the discussion with Zoran Skoda via E-Mail.
b) Ofer Gabber has sent me his proof and it is far more comprehensive, transparent and short than Rosenberg's.
c) It seems to me that this community is not a good place to report errors in preprints.

@Harry: In the comments to the question, Martin mentioned that he had emailed the author, but that the author was too busy.

I agree with Harry that the question should be undeleted. I think questioning and being critical is extremely important to mathematics, and that this forum IS a good place for reports of possible errors.

In response to the tone of the post. The first version was probably ok. The later iterations were a bit incendiary. I think it is better to be a bit less intense when suggesting there are issues. I think a good way of posting this sort of thing, is saying that you think there might be an error, rather than asserting that the result is incorrect. However, I am far from the politeness police. You can choose to be as aggressive as you wish, but I think the comments reflected a preference for politeness.

Regarding you emailing Rosenberg. I have spoken with him about this. Yes, he is busy right now and of the opinion that you can resolve your difficulties on your own with your advisor. He also told me that one of the issues is that you want a simpler proof in a specific setting. Since he has not thought about this simpler proof, it is not surprising that he not create one for you. As I told you in personal email, working through his machinery might be advantageous to you, even though it can appear daunting.

Please reopen the question for at least the reason that you can answer it after you understand Ofer Gabber's and Zoran Skoda's correspondence with you . Others(at least I) would be interested to hear these things.

DISCLAIMER: I do NOT speak for Rosenberg. I do NOT speak for the MO community. This is just my interpretation of the situation. I cannot answer the questions that you have asked, and unfortunately don't have time right now to attempt to.

I tend to agree with Andy; although I have in the past asked a question about an erroneous theorem in a book I was studying and one of the answers saved me potentially a lot of time. So I think that we should perhaps exercise caution and treat each case on its individual merits. I have no opinion on this particular question, though.

@Harry : Yes, absolutely. Allowing that kind of thing would be damaging for MO.

@Andy: I'm inclined to agree with Noah and Bryan on this. Could you explain your reasoning?

This is why "as long as it doesn't happen too often" was an important part of my conditions.

I strongly agree with Andy. The issue is not (just) getting bad questions. Rather, it is that one should always be very polite and cautious in pointing out possible mistakes in other peoples work, and a widely read professional forum does not lend itself to such politeness and caution.

An important point to remember is that claiming a new result, especially a significant one, involves putting oneself right out on the edge, and there is always the danger of coming a cropper. One has to be respectful of this. On the one hand, if you made a mistake in a paper, you would presumably rather not have people trumpeting this all over MO, but would prefer to get the chance to quitely withdraw the claim; it's just professional courtesy to offer the same opportunity to others. On the other hand, if you are incorrect in your claim of a mistake, then you look somewhat foolish, and the author accused of making a mistake may well get annoyed. It's better to prevent such possibilities by not initiating them in the first place.

There is a reason that experienced mathematicians begin questions about another person's work (even if they have their doubts) with the expression "I don't understand [such-and-such in your argument]", putting the fault on themselves, not the person whose work it is. If there really is a mistake, it will come out with patient questioning, and if not, one avoids having egg on one's face.

P.S. I think Noah's suggest question, "I don't understand step X", is fine. This is the kind of question people ask all the time. It is very different to an accusation of a mistake.

It seems like the only thing at issue here is how diplomatically the question is worded. Is that a fair assessment?

Dear Matt,

Ah, okay. I thought that was just a given. However, I didn't read Martin's question, so I don't know how he asked it. I have asked such questions on MO before, and I always presume that it is either my misunderstanding or a typo (the book I'm referencing has very terse proofs as well as a veritable multitude of typos (and by typo, I mean something more like "small (albeit confusing) error that is inconsequential to the conclusions of the proof")).

(The comment above has quadruply nested delimiters =X)

Martin-

The issue isn't this particular example and whether you were right or wrong. I think at this point, this thread is clearly about how we deal in general with discussing potential errors in papers on MO. I'm not sure we've hit an consensus yet, but it's turned to a general question about what happens next time around, not the merits of your case.

Preprints are public domain, and I think that their potential errors, as long as they are of wider interest, are a legitimate topic for public discussion. But I think that a wise person phrases such questions diplomatically.
Also, sometimes we (collectively as mathematicians) want to verify a high-profile proof quickly; and sometimes we need help understanding a proof, which the author might not be the best person to give. Not asking because of etiquette might impede our work.
On the high profile side (papers whose veracity might effect an entire subfield), I would discuss it on a blog, rather than on MO, so that people have the chance to discuss the paper and find the error(s) together, if they exist- checking a proof is discussion-y, therefore not really for MO.
On the "not understanding" side, I think this is perfect MO territory as a matter of fact. If, a few years ago, I could have asked on MO about a certain argument I didn't understand (not having the background in that field, tangential to the rest of a paper, but critical in the proof), I would have saved a tremendous amount of time I used, trying to build on a certain result whose proof was wrong. If you don't understand a critical step of an important proof (and have put some effort into understanding it), then for goodness-sakes, ask! Don't refrain from asking for fear of offending the author... and because an author's reply might make insufficient sense, MO becomes an extremely valuable resource.

You're right- I mis-spoke and said something obviously stupid.
What I meant to say was that, after you publish anything (a paper, a book, an article, a painting, a musical composition, an MO question), then it has a life independent of its authors. Anyone can read it, and anyone can have an opinion on it- and with citation, anyone can use it. It exists as itself, not as an extension of its creators.

A colleague of mine had one of his preprints appear in some obscure journal once to which he had not submitted it. They just took it and published it without asking. This caused him some trouble when he himself submitted the paper to a different journal, being unaware at the time what had happened. After this experience, he always puts a copyright notice on all his preprints. Whether this is a more or less effective way of dealing with the problem than academic sanctions is unknown to me.

A paper being public domain does not mean that anyone can just plagiarize from it, simply because academia deals with plagiarism by other means.

Your faith is touching...

Preprints need not be public domain, but published papes should be. Once you've obtained the "journal credit" you no longer should protect your work from being published without your consent. (And I certainly don't think that the inital publisher should control future use/publication of the work!)

@Harald - your story is the first time I've heard of a preprint (as opposed to a paper) being published without the author's permission. Was it published under your colleague's name? Or was it a straight-up plagiarism? If the latter then the publisher was violating your colleague's "moral rights" even if the preprint was in the public domain. (Well, in Europe. America has no notion of "moral rights".)

@WillieWong - I want my ideas to be spread far and wide -- I would be delighted beyond words if any of my work was ever republished. I don't see how the scruples of the publisher come into it...

Sam, I take issue with the phrase "America has no notion of moral rights" . Perhaps a rephrasing or clarification from you would help stave off a flame war.

Also (hypothetically adopting the intent I see behind the phrase), would you take the same delight if I republished your work and associated someone else's name with it rather than your own? I suspect not. I see how scruples come into it, and hope you will see it as well.

Gerhard "Smile When You Say That" Paseman, 2010.12.12

@grp, Harry - "Moral rights" is a technical term in the field of copyright. Please see http://en.wikipedia.org/wiki/Moral_rights_%28copyright_law%29

@grp - You are free to republish my work under my name, because my work is (almost completely) in the public domain. If you decide to publish my work under another person's name then I will bring that fact first to your attention (as I will assume some misunderstanding) and then to the attention of your employer. Regardless of what happens after that point I will be somewhat flattered that you chose my theorems and not, say, those of Gowers.

@Sam: Yes, I realize this. My comment was that copyright law is sufficiently strong in the US already. I have no desire to make it any stronger.

Sam, thank you for the clarification. I understand the statement better, but still take issue with it, especially upon reading this extract found at the link you kindly provided:

"While the United States became a signatory to the convention in 1988,
it still does not completely recognize moral rights as part of copyright law,
but rather as part of other bodies of law, such as defamation or unfair competition."

I suggest that your choice of words was executed with insufficient care, and that there is still a measure of unintended insult in the phrase. I won't press the matter any further though, and I do not ask for further clarification or rephrasing.

Also, to the earlier point of scruples, anyone who does not respect moral rights might change more than just the name. They may have their own interpretation of the ideas which, among a myriad of possibilities, might do the opposite of delighting you. Either you are assuming extreme consideration on the part of the hypothetical unscrupulous republisher, or I am seeing something you are not in this situation. I still imagine you would be concerned about the scruples of the republisher.

Thanks again for the clarification; I feel my points have been addressed.

Gerhard "Ask Me About System Design" Paseman, 2010.12.12

@grp - IANAL, nor do I live in the USA. From my reading on-line (haha!) I gather that moral rights are not supported by case law in the USA but are supported by case law in several European countries.

As regards "They may have their own interpretation of the ideas which, among a myriad of possibilities, might do the opposite of delighting you." let me simply reply with a well-known quote of Jefferson:

"If nature has made any one thing less susceptible than all others of exclusive property, it is the action of the thinking power called an idea, which an individual may exclusively possess as long as he keeps it to himself; but the moment it is divulged, it forces itself into the possession of every one, and the receiver cannot dispossess himself of it. Its peculiar character, too, is that no one possesses the less, because every other possesses the whole of it. He who receives an idea from me, receives instruction himself without lessening mine; as he who lights his taper at mine, receives light without darkening me."

and a quip of Howard Aiken's:

"Don't worry about people stealing an idea. If it's original, you will have to ram it down their throats."

@Harald - Well, that is incredible. Since legal recourse is probably useless and certainly expensive allow me to suggest that an academic solution is called for. If you give me the details of the story in some way I can verify, then I can promise to never submit to that journal.