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Background of my question is the following: I have found a solution for my question Smoothness Conditions for Planar “Mock-parametric” Spline Interpolation and while developing the solution, I encountered aspects of spline interpolation that I haven't seen documented:

  • calculation of interpolating splines via an iterative formula, that would also allow the calculation of splines from point-sequences that are infinite in both directions

  • a general solution for optimizing linear functionals on interpolating splines

now, as I am no professional mathematician and haven't published anything yet, I would like to communicate my results in a lightweight process, which would mean giving enough detail to make my findings checkable and applicable.

Question:

is acceptable to make an online publications sketchy, i.e. providing arguments instead of proofs, in first version and, to deliver what is missing in later editing e.g. upon feedback?

I'm thinking about putting the results on arXiv, but I would also be happy to put them on MO in a CW contribution; direct communication to interested people would also be an option to me.
Any suggestions in that respect are welcome

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  • $\begingroup$ I highly recommend asking professionals directly. If you write a summary that they can read in a few minutes, followed by a longer first draft (marked as such so they know what to spend time on), then you can reference these from your MathOverflow user page and in a brief request that you send them. If you were to send me (also a non professional) such a request, I might reply that I am not interested, but might make suggestions as to how to find interested people. If you can, get brief feedback from two sources or more. Gerhard "Get That Support Network Activated" Paseman, 2018.09.29. $\endgroup$ – Gerhard Paseman Sep 29 '18 at 14:45
  • $\begingroup$ @GerhardPaseman that is of also a good idea; I have to check, if I can contact my former numerics professor, but I was a long long time ago when I studied math. $\endgroup$ – Manfred Weis Sep 29 '18 at 14:55
  • $\begingroup$ Do as you wish. The point is to get practice approaching people and asking them, even ones you don't know, in a way that advances your goal. Again, many people will answer a brief request, and hopefully one or two will answer with information you can use. If you send me such a request, the answer I give may not tell you how to write a paper, but it might tell you how to write a request. Gerhard "From Will Jagy Correspondence School" Paseman, 2018.09.29. $\endgroup$ – Gerhard Paseman Sep 29 '18 at 15:22
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I presume that with "online" publication you have arXiv in mind. (For a journal it does not really make a difference whether it is online or not.) With regards to your question, the key difference between arXiv and a journal is not so much the absence of a refereeing process, but the fact that on arXiv you can post multiple revised versions. With a journal publication you get a chance to revise it after the referee reports come in, but once it's accepted no further revisions are possible.

So yes, you can submit incomplete papers to arXiv, and complete them later. The arXiv moderators will hold you to a certain standard, but if you are not submitting a proof of the Riemann hypothesis you should be OK.

There are risks and benefits with an early submission to arXiv. One benefit is that you can protect your priority. Another benefit is that you might receive helpful feedback on your findings. One risk is that a sloppy first version may damage your reputation a professional researcher. Another risk is that someone may build on your results (with proper attribution, of course), perhaps generalizing them or applying them in a different context, while you may have wanted to do that yourself.

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    $\begingroup$ "you can submit incomplete papers to arXiv, and complete them later." While I agree that you literally can do this, I think it is usually bad for one's reputation to do so. I think the norm is that it is okay to upload a preprint and then go back later to add a result which was missing from the first version (and perhaps in progress when the first version was written) but that it doesn't look good to upload a paper with content (proofs, definitions) obviously missing. $\endgroup$ – David E Speyer Sep 29 '18 at 13:43
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    $\begingroup$ I think a better solution would be to write a separate research announcement and put it on the arXiv, then write the paper. See arxiv.org/abs/1510.00438 for an example. $\endgroup$ – David E Speyer Sep 29 '18 at 14:01
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    $\begingroup$ @DavidESpeyer thanks for pointing me to the option of a research announcement; that will be the path I go to get my feet wet. $\endgroup$ – Manfred Weis Sep 29 '18 at 14:33
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    $\begingroup$ I disagree with the "protect your priority" statement here, at least in one interpretation. A paper with incomplete proofs does not establish priority over a later paper with complete proofs, in my opinion. Otherwise we will have people submitting things they have a good hunch how to prove before they actually prove them. $\endgroup$ – Brendan McKay Sep 30 '18 at 4:19
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    $\begingroup$ @BrendanMcKay : I think the intent of Carlo's remark is that the arXiv provides a trusted public timestamp, so if someone else claims an earlier date but cannot provide comparable public proof, you should be in good shape, even if that person's formal publication comes out before yours. But obviously, an arXiv preprint can only definitively establish priority for what's actually in the preprint itself. $\endgroup$ – Timothy Chow Sep 30 '18 at 19:42
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I personally regard an arXiv preprint as a usual article, just not refereed. One should be able to refer to it, hence it should contain full proofs. After you put your results with full proofs on arXiv, you will be able to write a short answer to your question (not necessarily as a CW) with a reference to your preprint. This acceptable; see this answer.

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