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Last year a paper on the ArXiV (Akhmedov) claimed that Thompson's group $F$ is not amenable, while another paper, published in the journal "Infinite dimensional analysis, quantum probability, and related topics" (vol. 12, p173-191) by Shavgulidze claimed the exact opposite, that $F$ is amenable. Although the question of which, if either, was a valid proof seemed to be being asked by people, I cannot seem to find a conclusion anywhere and the discussion of late seems to have died down considerably. From what I can gather, Shavgulidze's paper seems unfixable, while the validity of Akhmedov's paper is undecided (although it may of course be decided now).

So, does anyone know if either of these papers is valid?

Last year a paper on the arXiv (Akhmedov) claimed that Thompson's group $F$ is not amenable, while another paper, published in the journal "Infinite dimensional analysis, quantum probability, and related topics" (vol. 12, p173-191) by Shavgulidze claimed the exact opposite, that $F$ is amenable. Although the question of which, if either, was a valid proof seemed to be being asked by people, I cannot seem to find a conclusion anywhere and the discussion of late seems to have died down considerably. From what I can gather, Shavgulidze's paper seems unfixable, while the validity of Akhmedov's paper is undecided (although it may of course be decided now).

So, does anyone know if either of these papers is valid?