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 (r² + rc²), we derive a regular metric: f (r) = 1 - 2μr² / (r² + rc²) ^ (3/2), which is free from central singularities and asymptotically equivalent to Schwarzschild geometry. We then compute key observable quantities: - black hole shadow radius (bc) - photon sphere radius (rₚh) - innermost stable circular orbit (ISCO) All observables are expressed as functions of the core scale parameter rc. 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.