Structural Differentiation Gravity v1.3: Kerr-like Rotational Black-Hole Signatures from Anisotropic Structure

Structural Differentiation Gravity (SDG) proposes that gravity is not a fundamental interaction, but the manifestation of gradients in structural density within a relationally closed system. In this work (v1.3), we extend the SDG framework to axisymmetric configurations and demonstrate that rotation-like black hole signatures can emerge purely from anisotropic structure. We introduce a minimal structural field: C(r, θ) = 1 / (r² + r_c² + a² cos²θ) where the parameter a encodes anisotropic structural differentiation. Without introducing spacetime rotation explicitly, this model reproduces key Kerr-like observational features: - shadow displacement- photon ring shift- brightness asymmetry- parameter-dependent deformation These results suggest that rotation is not a primitive property of spacetime, but an emergent consequence of structural asymmetry. This repository contains: - the full manuscript (PDF)- a reproducible Python implementation- figure outputs corresponding to the paper This work is a phenomenological toy model intended to demonstrate structural emergence, not a full relativistic solution. Version: v1.3Author: Koji OkinoYear: 2026