Geometric Standard Model: Part VI. Higgs Vacuum Elasticity, Isometric Rigidity, and the Manifold Rupture Threshold

Abstract

In the constrained 3+1+2 multitemporal framework, the Higgs boson is not treated as an independent scalar particle, but as the macroscopic yield strength of the vacuum constraint field itself. Under the principle of Local Time Freezing, topological knots act as absolute rigid bodies (isometrically rigid) that cannot continuously deform to absorb stress. By projecting the 6-dimensional phase-space lock of the proton (6π^5) against the fundamental geometric coupling limit (α_geom^-1), we analytically derive the absolute bare mass scale of the Higgs boson. The strict geometric product yields a theoretical bare mass of approximately 128.31 GeV, deviating by only ~ 2.4% from the experimental value. This demonstrates that the Higgs scale is the deterministic macroscopic boundary where localized rigid topological tension exceeds the ultimate elastic capacity of the multitemporal manifold, offering a purely geometric resolution to the hierarchy problem.