Newton's Constant as a Time-Field Spectral Curvature: A Wheeler–DeWitt Closure Pathway

Newton’s gravitational constant G is traditionally treated as a fundamental parameter introduced empirically into gravitational theory. In this work, we develop a structured framework in which G emerges from the spectral and stability properties of a scalar time-field Θ embedded within an extended Wheeler–DeWitt formalism. The analysis reduces gravitational coupling to the curvature of an effective time-field potential evaluated at equilibrium, together with a stability-selected eigenmode closure condition. Specifically, we show that G can be expressed in terms of the second derivative of the constraint-induced effective potential, linking macroscopic gravitational behavior to the ground-state fluctuation of a time-field degree of freedom. The resulting formulation connects quantum ground-state structure, stability selection via a universal fixed point, and geometric closure into a single reduction pathway. While a complete first-principles numerical derivation of G is not yet claimed, the problem is reduced to a well-defined, computable quantity within mini-superspace quantum gravity: G ⟷ Veff′′(Θ0). This framework provides a concrete target for future analytical and numerical work, reframing the determination of Newton’s constant as a spectral curvature problem within the Wheeler–DeWitt constraint geometry.