  In this article we propose a new construction of the spatial scalar curvature
operator in (1+3)-dimensional LQG based on the twisted geometry. The starting
point of the construction is to express the holonomy of the spin connection on
a graph in terms of the twisted geometry variables, and we check that this
expression reproduces the spin connection in terms of triads in a certain
continuum limit. The spatial scalar curvature in terms of twisted geometry is
obtained by considering the composition of the holonomy of the spin connection
on the loops. With the twisted geometry parametrization of the holonomy-flux
phase space, we further express the holonomy of the spin connection and the
spatial scalar curvature on a graph in terms of fluxes. Finally, they are
promoted as well-defined operators by replacing the fluxes with ordered flux
operators.
