Integrable clusters
  The goal of this note is to study quantum clusters in which cluster variables (not coefficients) commute which each other. It turns out that this property is preserved by mutations. Remarkably, this is equivalent to the celebrated sign coherence conjecture recently proved by M. Gross, P. Hacking, S. Keel and M. Kontsevich 
Arkady Berenstein, Jacob Greenstein and David Kazhdan
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