The Geometric Origin of the Gravitational Constant

We present a geometric re-parameterization of the Newtonian gravitational constant by expressing it as the inverse square of a single dimensional tension scale. The formulation relies only on dimensional consistency and the measured value of , without introducing new physical parameters or assuming a specific dynamical model. In this representation, changes in gravitational coupling correspond directly to inverse-square changes in the scale itself. The approach provides an operational way to interpret through one derived quantity while remaining fully consistent with SI units and CODATA measurements.