  In this note we confirm the guess of Calegari, Garoufalidis and Zagier in
Arxiv 1712.04887 that $R_\zeta=c_\zeta^2$, where $R_\zeta$ is their map on
$K_3$ defined using the cyclic quantum dilogarithm and $c_\zeta$ is the Chern
class map on $K_3$.
