Structural Differentiation Cosmology with Projection Formalism: A Unified and Falsifiable Framework for Cosmic Acceleration and Structure

We present a unified framework combining Structural Differentiation Cosmology (SDC) with a projection formalism, establishing a direct connection between underlying structural dynamics and observable cosmological quantities. In this framework, cosmic acceleration is not interpreted as a physical dark-energy component, but as a projection effect arising from irreversible structural differentiation in a closed relational system. The model is constructed to remain observationally consistent with ΛCDM in the background expansion history, while predicting a systematic and unavoidable deviation in the growth of structure. We introduce a unified observable framework, including the Geometry–Growth Projection Test (GGPT), which provides a direct and falsifiable criterion to distinguish projection-based acceleration from physical acceleration. This approach bridges fundamental dynamics and observations within a single minimal structure, offering a testable alternative to standard cosmology. If no geometry–growth separation is observed, the framework is ruled out.