Scale-Invariant Theory of Cosmic Dilution and Local Resistance Mechanism: A Unified Solution to the Mass Gap and Proton Radius Puzzle

In modern physics, the "Mass Gap Problem" in Quantum Chromodynamics (QCD) and the "Cosmological Constant Problem" (the 120-order-of-magnitude discrepancy) in cosmology have been regarded as the two greatest independent unsolved problems. This paper demonstrates that these are phenomena stemming from a single root cause, attributed to overlooking the "geometric nature of space as a medium." We propose the SIT (Scale-Invariant Theory), which defines space itself as a dynamic medium that continues to multiply and dilute based on a scale-invariant algorithm. First, regarding the 120-order discrepancy between the theoretical and observed values of vacuum energy density, we resolved this mathematical divergence by applying a dilution calculation using the geometric growth rate of space (N = 27) and defining the current universe as being in the 86th generation. Second, we defined mass as the "equilibrium between spatial expansion pressure and local resistance" and presented the SIT Equilibrium Equation based on Cauchy's surface area formula. The theoretical proton radius derived by substituting the proton mass into this equation, r ≈ 0.84124 fm, aligns with the latest muonic hydrogen experimental values and the CODATA 2018 recommended value with astounding precision (0.02% error). This study identifies the physical origin of the mass gap in hadrons and provides a new physical model that unifies the description of the quantum scale and the cosmic scale.