Structural Differentiation Gravity: Observable Signatures of Regular Black Holes

This work presents a minimal and fully reproducible observational extension of Structural Differentiation Gravity (SDG), focusing on black hole observables. Starting from a single structural density function, C(r) = 1 / sqrt(r^2 + r_c^2), we derive a regular metric: f(r) = 1 - 2μr^2 / (r^2 + r_c^2)^(3/2), which is free from central singularities and asymptotically equivalent to Schwarzschild geometry. We then compute key observable quantities:- black hole shadow radius (b_c)- photon sphere radius (r_ph)- innermost stable circular orbit (ISCO) All observables are expressed as functions of the core scale parameter r_c. The model predicts systematic deviations from General Relativity, providing a direct observational testing framework. All figures are fully reproducible using the provided Python script. --- Key statement: Geometry is not fundamental.It is the shadow of structure.