[This](http://arxiv.org/abs/1310.0989v4) arXiv paper is claimed to contain a proof for the MMS conjecture. But it seems that this manuscript is not yet peer reviewed by other mathematicians. I personally tried to follow the paper, but after some point I couldn't due to the lack of explanation, or my ability to understand. Given the interest of mathematicians for this problem, I think the manuscript could have been noticed by mathematicians' community. What is the status of this paper?



Is the Manickam-Miklós-Singhi Conjecture solved?
I am aware of the paper, but I am not sure that MO is the right forum for this sort of question. Nonetheless, let me try to provide some information in as neutral a manner as possible. 


Note that there has been a flurry of recent activity concerning the MMS conjecture. Indeed, a paper of Huang and Sudakov *just* appeared in the [Electronic Journal of Combinatorics](http://www.combinatorics.org/ojs/index.php/eljc/article/view/v21i3p7). Their main result implies a cubic bound for MMS and it also resolves the vector space analogue of MMS. There is also a very recent [paper](http://www.math.cmu.edu/~ameera/research/MMSVecSet.pdf) of Chowdhury, Sarkis and Shahriari which has better bounds than the Huang and Sudakov paper. This paper was recently accepted by JCTa, and will appear soon. Finally, there is a [paper](http://arxiv-web3.library.cornell.edu/pdf/1308.2176.pdf) by Prokovskiy which proves that the MMS conjecture holds when $n \geq 10^{46}k$. As far as I know, this paper is still under review and has not been accepted yet. This summary is by no means comprehensive. 


Regarding the Blinovsky [paper](http://arxiv.org/pdf/1310.0989v4.pdf), the actual strategy is to prove a stronger statement, namely the Ahlswede-Khachatrian conjecture (up to a finite number of exceptions). The remaining cases can then be checked by computer. An earlier [paper](http://link.springer.com/article/10.1134%2FS0032946012040059#page-1) by Aydinian and Blinovsky proves that MMS does indeed follow from Ahlswede-Khachatrian. This paper has already appeared. 


Finally, note that the Blinovsky paper is not cited in the above Huang and Sudakov paper, and that in the Chowdhury, Sarkis and Shahriari paper, MMS is still listed as an open problem. Of course this does not mean the paper is necessarily incorrect. I think we will just have to wait and let the peer-review process play itself out. 


