A paper claiming a solution to the Feder-Vardi conjecture appeared yesterday on the arXiv:
Tómas Feder is the third author. (However, I noticed that the order of the authors in the version of the paper Feder posted on his web page is different from the one used in the arXiv version.)
The authors have also posted two videos on YouTube:
If the technical content of the paper is found to be correct by the community working on CSPs after careful peer review, this is a truly major result.