Background of my question is the following: I have found a solution for my question [Smoothness Conditions for Planar “Mock-parametric” Spline Interpolation](https://mathoverflow.net/questions/271043/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:**
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> 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?
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> 


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



How Much Flesh to the Bones does an Initial Online Publication need?
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.


