  We demonstrate quantum critical scaling for an $S=1/2$ Heisenberg
antiferromagnetic chain compound CuPzN in a magnetic field around saturation,
by analysing previously reported magnetization [Y. Kono {\it et al.}, Phys.
Rev. Lett. {\bf 114}, 037202 (2015)], thermal expansion [J. Rohrkamp {\it et
al.}, J. Phys.: Conf. Ser. {\bf 200}, 012169 (2010)] and NMR relaxation data
[H. K\"uhne {\it et al.}, Phys. Rev. B {\bf 80}, 045110 (2009)]. The scaling of
magnetization is demonstrated through collapsing the data for a range of both
temperature and field onto a single curve without making any assumption for a
theoretical form. The data collapse is subsequently shown to closely follow the
theoretically-predicted scaling function without any adjustable parameters.
Experimental boundaries for the quantum critical region could be drawn from the
variable range beyond which the scaled data deviate from the theoretical
function. Similarly to the magnetization, quantum critical scaling of the
thermal expansion is also demonstrated. Further, the spin dynamics probed via
NMR relaxation rate $1/T_1$ close to the saturation is shown to follow the
theoretically-predicted quantum critical behavior as $1/T_1\propto T^{-0.5}$
persisting up to temperatures as high as $k_\mathrm{B}T \simeq J$, where $J$ is
the exchange coupling constant.
