Structural Differentiation Cosmology (SDC) v1.2: A Decisive Observational Test via the Geometry–Growth Projection Test (GGPT)

We present Structural Differentiation Cosmology (SDC) v1.2, a minimal and falsifiable framework in which cosmological observables arise as projections of irreversible structural differentiation within a closed relational system. In contrast to standard cosmology, SDC does not introduce additional physical components such as dark energy. Instead, it reinterprets observed phenomena as consequences of internal structural evolution. We demonstrate that SDC reproduces the observed expansion history H(z) with near-degeneracy relative to ΛCDM, while simultaneously predicting a systematic suppression in structure growth fσ₈(z). This separation leads to a key observational insight: Background expansion alone does not uniquely determine the underlying physical mechanism. To resolve this degeneracy, we introduce the Geometry–Growth Projection Test (GGPT), a unified diagnostic in the (ΔH/H, Δ(fσ₈)/(fσ₈)) plane. This provides: A single decisive and directly testable observational criterion distinguishing structural projection cosmology from physical acceleration models. We further show that both expansion and growth are governed by a single structural variable C(z), establishing a unified dynamical origin. Key result:Geometry agrees, but growth reveals the underlying structure. SDC therefore shifts cosmology from an energy-component description to a structural evolution description, providing a direct and testable bridge between theory and observation.