The mysterious “colleagues” that forced Akhmedov to withdraw his paper once is Victor Guba, who constructed counterexamples to both main non-amenability statements of the paper. I know all that because both Akhmedov and Guba copied their messages to me. There is also a newer counterexample for the new (April) version of the paper and Akhmedov promised to withdraw the paper, although he has not done it yet. As I understand from Guba’s comments, there is nothing reasonable in Akhmedov’s approach, and the paper is written in an almost unreadable way. The full paper by Shavgulidze, on the other hand, allows line-by-line checking, and if there are no serious errors in the computation, it should be correct. I checked the main line of the proof myself. Guba is reading the text and has found several misprints and miscalculations which all have been corrected in the newer version of Shavgulidze’s text.