This paper systematically integrates the three progressive tiers of the H-SET quantum theoretical system---the perturbative quantum framework, the spatial quantum phase transition theory, and the non-perturbative quantum computational framework---into a unified architecture that spans from the spatial elastic field to the mass spectrum of all Standard Model particles. The perturbative framework establishes the exact propagator of the spatial density potential, proving renormalizability and ultraviolet completion via an asymptotically safe fixed point. The spatial quantum phase transition theory constructs the coupled FRG equations and identifies the solidification phase transition universality class. The non-perturbative quantum computational framework completes the first-principles calculation of all elementary particle masses. The three tiers are connected by the asymptotically safe fixed point, the instanton condensation mechanism, and the elastic-torsion self-consistency condition. The entire quantum theoretical system depends only on the two global fitting parameters of H-SET, with all other parameters derived from theory. This paper serves as the compendium of the H-SET quantum theory system.
Changxi Hong (Thu,) studied this question.