Dynamic Phase Transition of the Barbero-Immirzi Parameter: A Hypertensor Fluid Model within SMT

The most challenging mathematical anomaly in fusing Loop Quantum Gravity (LQG) and Quantum Hydrodynamics (QHD) is the dynamical behavior of the Barbero-Immirzi parameter (γImmirzi). Previous theories encountered logical contradictions by forcing this discrete spin network constant to arbitrarily ’run’ as a macroscopic hydrodynamic variable.To resolve this paradox, this paper introduces Space-Time Mapping Theory (SMT) and Hypertensor Field Theory. We promote the entropy flow of the quantum fluid (ns) from a scalar wave function to a higher-order hypertensor fluid T_αβ···^µν··· .Consequently, we rigorously prove that γImmirzi is not a simple coupling constant, but a ’Global Topological PhaseTransition Factor’ that smoothly maps the discrete quantum lattice onto the continuous macroscopic spacetime under extreme curvature.