Part 5_The Geometric Origin of Inverse-Square Scaling in the Gravitational Constant
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2026
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| _version_ | 1866901853388668928 |
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| author | Hong, Seunghyun |
| author_facet | Hong, Seunghyun |
| contents | <p><a title=" Part 5_The Geometric Origin of Inverse-Square Scaling in the Gravitational Constant" href="https://youtu.be/Q4d-a3yJfLo?si=v_lerb6031QxElrV" target="_blank" rel="noopener">https://youtu.be/Q4d-a3yJfLo?si=v_lerb6031QxElrV</a></p> <p><a title="Part 5_왜 힘은 1/r²로 줄어드는가? ― 중력의 역제곱 법칙, 기하학에서 나오다" href="https://youtu.be/o_iy4mY78xM?si=nU8VzEl5LNZl4A4J" target="_blank" rel="noopener">https://youtu.be/o_iy4mY78xM?si=nU8VzEl5LNZl4A4J</a></p> <p>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.</p> <p><br>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).</p> <p><br>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.</p> <p><br>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.</p> <p><br>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.</p> <p><br>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.</p> <p><br>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.</p> <p> </p> <p> </p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18447514 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Part 5_The Geometric Origin of Inverse-Square Scaling in the Gravitational Constant Hong, Seunghyun Inverse-square law Gravitational scaling Gravitational Gravitational waves Geometric origin Shell hierarchy Discrete geometry Flux conservation Spherical symmetry Quartic scaling Discrete-to-continuum Structural derivation Junctional Sphere Self-Regulated Curvature Dynamics <p><a title=" Part 5_The Geometric Origin of Inverse-Square Scaling in the Gravitational Constant" href="https://youtu.be/Q4d-a3yJfLo?si=v_lerb6031QxElrV" target="_blank" rel="noopener">https://youtu.be/Q4d-a3yJfLo?si=v_lerb6031QxElrV</a></p> <p><a title="Part 5_왜 힘은 1/r²로 줄어드는가? ― 중력의 역제곱 법칙, 기하학에서 나오다" href="https://youtu.be/o_iy4mY78xM?si=nU8VzEl5LNZl4A4J" target="_blank" rel="noopener">https://youtu.be/o_iy4mY78xM?si=nU8VzEl5LNZl4A4J</a></p> <p>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.</p> <p><br>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).</p> <p><br>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.</p> <p><br>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.</p> <p><br>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.</p> <p><br>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.</p> <p><br>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.</p> <p> </p> <p> </p> |
| title | Part 5_The Geometric Origin of Inverse-Square Scaling in the Gravitational Constant |
| topic | Inverse-square law Gravitational scaling Gravitational Gravitational waves Geometric origin Shell hierarchy Discrete geometry Flux conservation Spherical symmetry Quartic scaling Discrete-to-continuum Structural derivation Junctional Sphere Self-Regulated Curvature Dynamics |
| url | https://doi.org/10.5281/zenodo.18447514 |