Before revision:  The clan embedding has multiplicative distortion t if for every pair  x,y  some copy y'\in f(y) in the clan of y is close to the chief of x: \min_{y'\in f(y)}d(y',\chi(x))\le t\cdot d(x,y).
After revision:  The clan embedding has multiplicative distortion t if for every pair ( x,y some copy y'\in f(y) in the clan of y is close to the chief of x: \min_{y'\in f(y)}d(y',\chi(x))\le t\cdot d(x,y).