Newton’s gravitational constant G is traditionally treated as an empirical parameter with no known first-principles derivation. This work presents a structured reduction framework in which gravitational coupling emerges from the spectral properties of a dynamical time field. Within this approach, G is expressed as: G=c5ℏΩ12,G where Ω1 is the lowest stable eigenfrequency of a time-field Hamiltonian. This formulation reduces the problem of deriving G to the independent determination of a single quantity: a fundamental time-field wavelength λΘ. A dimensionless stability constant x≈0.5512855984 is introduced as a fixed point governing the balance between coupling and damping in time-field dynamics. This parameter connects pre-stabilized frequency scales to observable structure and provides a mechanism for selecting physically stable configurations. The framework is explicitly falsifiable. It predicts that gravitational coupling may exhibit small environment-dependent deviations arising from local gradients in the time field. These deviations provide a potential experimental signature distinguishing this model from standard gravitational theory. This work does not claim a completed first-principles derivation of G, but instead establishes a minimal, mathematically consistent, and testable pathway by which such a derivation may be achieved. The decisive remaining step is the independent derivation of the fundamental time-field scale from intrinsic dynamics.
Matthew Hall (Mon,) studied this question.