This paper serves as the concluding study of the ”Topological-Gauge Duality”series, focusing on translating the previously constructed theoretical framework andmathematical proofs into testable physical predictions and experimental proposals.It proposes using the thermal Hall effect in condensed matter systems as a keyprobe for topological order, with its quantized coefficient mappable to the neutralcurrent algebra in gauge theory. Through a reanalysis of lattice Quantum Chromodynamics (QCD) data, a scaling relation between instanton number density andthe mass gap is revealed, providing indirect yet solid evidence for the topologicalmechanism. Furthermore, a quantum simulation scheme based on optical latticecold atoms is designed to realize U(1) and SU(2) gauge fields and detect their topological mass gap. Finally, by integrating the series’ findings, a cross-disciplinaryresearch program is constructed, merging high-energy physics, condensed matterphysics, and quantum information, elucidating its profound significance for solvingthe Yang-Mills mass gap problem and promoting the unification of physics.