  In \cite{Park:2014tia} we proposed a way of quantizing gravity with the
Hamiltonian and Lagrangian analyses in the ADM setup. One of the key
observations was that the physical configuration space of the 4D
Einstein-Hilbert action admits a three-dimensional description, thereby making
gravity renormalization possible through a metric field redefinition.
Subsequently, a more mathematical and complementary picture of the reduction
based on foliation theory was presented in \cite{Park:2014qoa}. With the setup
of foliation the physical degrees of freedom have been identified with a
certain leaf. Here we expand the work of \cite{Park:2014qoa} by adding another
mathematical ingredient - an element of jet bundle theory. With the
introduction of the jet bundle, the procedure of identifying the true degrees
of freedom outlined therein is made precise and the whole picture of the
reduction is put on firm mathematical ground.
