Part 5The Geometric Origin of Inverse-Square Scaling in the Gravitational Constant

https: //youtu. be/Q4d-a3yJfLo? si=vₗerb6031QxElrV https: //youtu. be/oᵢy4mY78xM? si=nU8VzEl5LNZl4A4J In this work, we present a geometric interpretation of the inverse-square scaling associated with the gravitational constant, derived within the SRCD (Self-Regulated Curvature Dynamics) framework. Rather than postulating the inverse-square law as a fundamental dynamical principle, we show that this scaling emerges naturally from the shell hierarchy formed by discrete spherical units—JS (Junctional Spheres) and their composite organization into SH (Shell Hierarchies). By constructing a discrete shell structure and examining the ratio between adjacent shells, we obtain a quartic shell-mapping relation. When interpreted in three-dimensional space, this relation implies an effective radial scaling proportional to the square root of the shell index. Independently, the requirement of conserved geometric throughput (or flux) across spherical shells fixes the radial density to scale inversely with the surface area. Taken together, these two ingredients—shell geometry and conservation across shells—lead directly to an inverse-square radial dependence, without assuming any force law, field equation, or phenomenological input. Importantly, this work does not propose a modification of Newtonian gravity, nor does it introduce a new coupling constant. Instead, it provides a structural explanation for why inverse-square scaling appears so robust and universal across gravitational phenomena. The result suggests that the inverse-square form traditionally attributed to gravity can be understood as a geometric consequence of discrete shell organization and conservation, rather than as an independent postulate. This paper is intended as a geometric and structural analysis. Broader conceptual interpretations of JS and SH within the SRCD worldview will be presented separately.