Paper 45:Spatial Quantum Phase Transition Theory and Non-perturbative FRG Numerical Implementation: From Instanton Condensation to Quark Confinement

While the non-perturbative quantum computational framework of H-SET has successfully calculated the masses of all elementary particles, several core parameters have until now relied on experimental calibration. This paper systematically establishes the functional renormalization group framework for the spatial quantum phase transition theory, deriving these parameters from first principles. We construct coupled shear-torsion FRG equations and numerically solve the complete renormalization group flow of the torsion elastic modulus across 18 orders of magnitude, from the Planck scale to the hadronic scale. Using an instanton liquid model, we derive the torsion self-coupling constant independently, obtaining a value of approximately 1.61, which deviates merely 0.6 percent from the value calibrated by the muon mass. We further derive the quark confinement string tension from the FRG framework, obtaining a value consistent with QCD experimental data. The spatial solidification phase transition is identified as belonging to the three-dimensional XY universality class with a critical exponent of approximately 0.35, explaining the physical origin of the maximal winding number of three that underlies the existence of exactly three generations of fermions.