Structural Differentiation Cosmology (SDC): Growth-Index Signatures and a Decisive Observational Test

Version 1. 7 of Structural Differentiation Cosmology (SDC). This work proposes an alternative cosmological interpretation in whichthe observed cosmic acceleration is not a dynamical expansion drivenby dark energy but an observational projection emerging from irreversibleinternal structural differentiation in an externally closed universe. The framework remains nearly degenerate with ΛCDM at the level of thebackground expansion history while predicting a systematic deviationin the growth sector. This version reformulates the SDC–ΛCDM distinction in terms of threelinked observational signatures: • the growth index γ• the growth observable fσ8 (z) • the geometry–growth consistency observable EG (z) The theory predicts a small but coherent suppression in fσ8 (z) and asystematic drift in EG (z), while remaining consistent with currentobservations. A decisive observational discrimination is predicted at higher redshift, which can be tested by upcoming surveys such as Euclid and the NancyGrace Roman Space Telescope. All figures and analysis scripts used in this work are included in therepository. This repository corresponds to the research paper: Structural Differentiation Cosmology (SDC): Growth-Index Signaturesand a Decisive Observational Test (v1. 7).