The Longest-Term Prediction in Cosmology and Fundamental Physics: The Evolution of the Proton-to-Electron Mass Ratio mp/me

One of the most persistent mysteries in physics is the origin and potential time evolutionof the proton-to-electron mass ratio mp/me ≈ 1836.15. For nearly a century, this number hasresisted theoretical explanation and remains an arbitrary parameter in the Standard Model.The anthropic principle explains why we observe a value compatible with life, but it does notexplain why it has exactly this value. In the Theory of Hyperbolic Unity (THUI), we propose a different view: mp/me is not afixed constant but a dynamic quantity arising from the geometry of a dual vacuum. The localcubic layer (finite, rigid) and the nonlocal hyperbolic layer {5, 3, 3} (infinite, expanding) arelinked by resonance 1729. The slow unfolding of the vacuum, governed by the cubic curvaturecorrection R3, leads to a gradual decrease in the mass ratio over cosmic time. We derive the evolution equation for mp/me(t) and provide numerical predictions for thenext 10–1000 billion years. The change is extremely slow (on the order of 10−18 per year atpresent), but directional and, in principle, testable with future ultra-precise laboratory andastrophysical measurements. This makes the evolution of mp/me one of the longest-term yetpotentially observable predictions in the history of cosmology and fundamental physics. If confirmed, it would open a direct observational window into the dynamics of vacuumduality and the geometric origin of particle masses.