<p>This paper focuses on a phase
transition from the asymptotic safety approach of renormalizing the quantum
gravity (QG) to a more granular approach of the loop quantum gravity (LQG) and
then merging it with the Regge calculus for deriving the spin-(2) graviton.
From loop-(2) onwards, the higher derivative curvatures make the momentum go to
infinity which assaults a problem in renormalizing the QG. If the Einstein-Hilbert (E-H) action, is
computed, and a localized path integral (or partition functions) is defined
over a curved space, then that action is shown to be associated with the higher
order dimension in a more compactified way, resulting in an infinite winding
numbers being accompanied through the exponentiality coefficients of the
partition integrals in the loop expansions of the second order term onwards.
Based on that localization principle, the entire path integral got collapsed to
discrete points that if corresponds the aforesaid actions, results in negating
the divergences’ with an implied bijections’ and reverse bijections’ of a
diffeormorphism of a continuous differentiable functional domains. If those
domains are being attributed to the spatial constraints, Hamiltonian
constraints and Master constraints then, through Ashtekar’s variables, it can
be modestly shown that the behavior of quantum origin of asymptotic safety is similar
to the LQG granules of spinfoam spacetime. Then, we will proceed with the
triangulation of the entangled-points that results in the inclusion of Regge
poles via the quantum number (+2,-2,0) as the produced variables of the
spin-(2) graviton and spin-(0) dilaton.</p>