How to cite Babai's new graph isomorphism result? Recently, Babai has published a paper on STOC 2016 claiming that graph isomorphism can be solved in quasipolynomial time. 

In the beginning of 2017, Babai retracted the quasipolynomial claim due to some serious mistakes found by Harald Helfgott. As explained by Babai himself, this flaw makes the improvement more modest in terms of running time. 

About 5 days after retracting the quasi-polynomial claim, Babai posted another update in his homepage arguing that he had fixed the flaw in the proof, restoring in this way the quasi-polynomial running time. 

I have to say that after this fast change on the status of the correctness of the proof I would normally completely ignore the new paper until it was published in a well respected journal. 

But since Babai is Babai, most of the community is taking his's word for granted, at least publicly, even though the new version of the paper with all corrections implemented is not even available. Note that even great people make mistakes and there is a non-negligible chance that the new fix also has a flaw and so on. 

So now, how should I cite the new result? 


Cite the STOC paper claiming the quasipolynomial upperbound. 
Cite the STOC paper explaining that it has a serious flaw and that the real running time improves the previous subexponential lower bound. 
Cite the STOC paper saying that it had a flaw that was fixed by Babai. 
Do not cite at all, and state the old upper bound of $2^{O(\sqrt{n})}$ as the current established upper bound.
First off, I would discourage submitting for publication an unconditional paper which depends on the quasi-polynomial result, if that's what you want the citation for. Rephrase the result as conditional upon the the existence of a quasi-polynomial GI algorithm and state in a footnote that Babai may have proven this but that the paper is not publicly available. In this case, no citation is necessary because you don't need the result for the paper.

In any other context, I don't think it's particularly necessary to cite an available paper - citing his website is fine. It depends a little on what you are writing, but I would recommend asserting something along the lines of "it is widely believed that GI is solvable in quasipolynomial time and a proof of this has been announced by Laszlo Babai [citation to the webpage where he makes the claim]."

One notable advantage of citing his online claim is that his website contains both his own words as to the current claim and a link to his preprint.