Time-Density Field Theory III: Vacuum Normalization, Fundamental Scale ν0, and the Relation between Gand h

We develop a refined formulation of time-density field theory by introducing a physical interpretation of the fundamental time-density scale ν0 and its relation to vacuum energy density. A central result of this work is that the gravitational constant Gand Planck constant hmay be connected through the relation h = (2π c⁵) / (G ν₀²) suggesting that these constants are not fundamentally independent, but arise from a common underlying scale associated with the vacuum time-density field. To support this interpretation, we introduce a two-stage normalization scheme. First, the vacuum energy density is fixed as a reference state, defining a dimensionless normalization of the time-density field. Second, a high-energy scaling relation of the form ρν = γ (h / c³) ν⁴ is adopted, allowing the vacuum energy density to determine the fundamental scale ν0. Within this framework, the vacuum energy density, the time-density scale, and the constants G and h become mutually connected. This leads to a unified interpretation in which gravity, quantum behavior, and vacuum structure emerge as different aspects of a single underlying time-density field. Although the present work does not yet provide a complete dynamical derivation, it establishes a consistent and physically motivated framework that may serve as a basis for further development toward a unified theory of quantum gravity.