In this post and this one,, I mentioned a paper by Arash Rafiey, Jeff Kinne and Tomás Feder and one by Andrei Bulatov, claiming a solution to the long-standing Feder-Vardi dichotomy conjecture. Today Moshe Vardi pointed out to me this paper by Dmitriy Zhuk that offers a third proof of that conjecture.
At this point, I think that one can safely say that the dichotomy conjecture is
true. Indeed, I find it hard to believe that all the three proofs contain
mistakes that cannot be patched. As I wrote in my earlier posts on this matter, I hope all the proofs will be found to be correct by the community and that the techniques used in those articles will find application in other contexts.
Congratulations to the authors of those papers!