Empirical Resolution of the Vacuum Energy Discrepancy through cG$\hbar$H$_0$ Physics

The cosmological constant problem represents one of the most significant discrepancies in modern physics, with quantum field theory predictions for the vacuum energy density exceeding observational values by approximately 120 orders of magnitude. We propose a phenomenological framework extending the Bronstein cube of cG$\hbar$ physics to include the Hubble constant H$_0$, termed cG$\hbar$H$_0$ physics. This approach empirically relates the gravitational constant G to fundamental scales in quantum mechanics, relativity, and cosmology, yielding expressions for the vacuum energy density $\rho_{\rm vac} \approx H_0^2 / G$ and nuclear density $\rho_{\rm nucleus} \approx H_0 \Omega_n / G$, where $\Omega_n = m_n c^2 / \hbar$ and $m_n$ is the nucleon mass. These relations bridge microscopic and macroscopic scales, suggesting that the smallness of the observed vacuum energy arises naturally from the interplay of these constants, without requiring fine-tuning. Numerical verifications confirm the approximations align with empirical data within factors of order unity. This framework may inspire dynamical theories where cosmology regulates quantum vacuum contributions.