Structural Gravity Theory v1.0: Gravity as Emergent Structural Constraint Generated by Incomplete Differentiation

Structural Gravity Theory (SGT) v1.0 proposes that gravity is not a fundamental interaction but emerges from structural constraint generated by incomplete differentiation of structure. The theory introduces the structural constraint C = R − D where R is the required differentiation and D is the realized differentiation. Structural constraint obeys a local conservation law ∂C/∂t + ∇·J_C = S_C, with the vacuum limit (S_C = 0) leading, together with spherical symmetry, to the emergence of the inverse-square law. The structural constraint field χ satisfies ∇²χ = κ_C C, which generates the structural potential Φ = Φ_b + χ and the gravitational field g = −∇Φ. Newtonian gravity appears naturally as the weak-field limit |χ| ≪ |Φ_b|, while black holes are interpreted as states of maximum structural constraint, characterized by the structural locking parameter Γ = C/R → 1, which defines a structural horizon corresponding to the Schwarzschild radius. The manuscript develops the theory through a constructive sequence from structural postulates to differentiation, constraint, conservation, gravity, kinematics, the Newtonian limit, the vacuum limit, the black hole limit, and a unified structural framework. The manuscript consists of 17 sections, with Sections 2–13 corresponding one-to-one with Figures 1–12, allowing the complete theory to be followed directly through the accompanying figures. This repository contains: Structural_Gravity_Theory_v1.0.pdf Figures 1–12 (PNG) README LICENSE This work is released as a scientific preprint under the Creative Commons Attribution 4.0 International (CC BY 4.0) license.