Deformed Hamiltonian Constraint and UV Spectral Dimension Flow in SU(2) Lattice Gravity

This paper investigates the ultraviolet (UV) behavior of SU(2) Lattice Gravity by analyzing a deformed Hamiltonian constraint. Through the derivation of the spectral dimension, we demonstrate a dynamical dimensional reduction phenomenon where the effective spacetime dimension flows from ds = 4 in the macroscopic infrared regime down to ds = 2 at the UV fixed point. This framework provides a consistent algebraic description of quantum geometry at Planckian scales without relying on external background structures.