Structural Differentiation Gravity and Regularized Black Hole Geometry: From Structural Density to Metric (v1.1)

This work presents a minimal and fully closed derivation of a regular black-hole geometry within Structural Differentiation Gravity (SDG). In this framework, gravity is not treated as a fundamental interaction, but emerges as the gradient of structural density. Starting from a single structural density function, we derive gravitational acceleration, an effective mass profile, and the corresponding metric function without introducing any additional degrees of freedom. The resulting geometry is regular at the center and asymptotically reduces to the Schwarzschild solution. This suggests that singularities are not physical entities, but artifacts of incomplete description. All figures in the paper can be reproduced using the provided Python script. --- Key idea: Gravity is not sourced — it is revealed by structural gradients. Mass is not fundamental — it is a projection of structure. Black holes are not singularities. They are saturation states of structural differentiation.