The Topology Residual Entropy Increase Theory (TRT) takes the "right-handed cylindrical helicalmotion of space at the speed of light" ( ) as its sole foundational axiom. Through a threelayer topological expansion ( , ) and five residualiterations, it achieves a self-consistent closed loop for the fundamental constants and physicalquantities , , , , , , as well as the Hawking temperature and Bekenstein-Hawkingentropy of black holes.This paper systematically demonstrates, from five independent dimensions—geometric-topologicalnecessity, dimensional self-consistency and residual bridging, the critical balance criterion (cancellation when ), high consistency with experimental values, and minimality of selfconsistency—that the "three-layer + five-iteration" structure is the unique minimal structure withinthe current framework that simultaneously satisfies geometric self-consistency, dimensionalclosure, critical balance, and experimental agreement. In addition, the theory naturally derives theholographic property of space (with residual networks serving as holographic carriers, and blackhole event horizons as well as large-scale cosmic structures acting as effective holographicscreens). It also proposes a series of falsifiable predictions, including an upper geometric limit onthe Hawking temperature of Planck-mass black holes, the Bekenstein-Hawking entropy of Planckmass black holes approaching , and the linking number of early-universe residual networksdecaying as . These predictions provide clear directions for testing with LISA, gamma-raytelescopes, and CMB observations. This paper serves as a phased summary of the TopologyResidual Unified Field Theory series and lays a solid theoretical foundation for subsequentprediction verification, cosmological applications, and experimental design.