  In [F] H. Furusho proves the beautiful result that of the three defining
equations for associators, the pentagon implies the two hexagons (see also
[W]). In this note we present a simpler proof for this theorem (although our
paper is less dense, and hence only slightly shorter). In particular, we
package the use of algebraic geometry and Groethendieck-Teichmuller groups into
a useful and previously known principle, and, less significantly, we eliminate
the use of spherical braids.
