Structural Differentiation Gravity (SDG) v2.0: A Minimal and Falsifiable Structural Formulation of Gravity

Structural Differentiation Gravity (SDG) v2.0 proposes a minimal and closed formulation of gravity based on structural differentiation. Instead of treating gravity as a force sourced by mass, SDG interprets gravitational dynamics as the observable manifestation of structural gradients and connections within a relational configuration. The theory is defined by a minimal equation: g = -α∇C + β(∇×Γ) where:C represents structural density, andΓ represents structural connection. This formulation provides: • A Helmholtz-complete decomposition of gravity into gradient and rotational components • A framework independent of explicit mass sources • A direct link to observational tests via the Geometry–Growth Projection Test (GGPT) A key prediction is: Even if cosmic expansion matches ΛCDM (H(z)), structure growth must deviate: Δfσ8(z) ≠ 0 This provides a decisive observational criterion distinguishing structural projection from physical acceleration. Core thesis: Gravity is the manifestation of structural differentiation. Gradients and connections are its observable projections. Cosmic acceleration and gravity share one structural origin. This work presents a minimal, falsifiable alternative to standard interpretations of gravity and cosmic acceleration.