Structural Cosmology v1.3: A Structural Differentiation Framework for Cosmic Structure Formation

Structural Cosmology v1.3 presents a phenomenological framework in which a single structural field, Δ, governed by the potential V(Δ) = (1/2)m²Δ² − (λ/4)Δ⁴ generates three dynamical regimes associated with Dark Energy (Differentiation), Observable Matter (Transition), and Dark Matter (Cohesion). Building upon Structural Cosmology v1.0–v1.2, this release extends the framework from theoretical foundations and parameter constraints to a comprehensive observational comparison program. A Difference–Gradient–Reconstruction (DGR) pipeline is introduced to connect structural dynamics with cosmological and astrophysical observables, including expansion history, effective equation of state, matter power spectra, growth rates, weak lensing, galactic rotation curves, and halo density profiles. The paper develops a falsifiability architecture (C1–C20), illustrative joint parameter constraints, cross-scale consistency analysis, likelihood-based parameter updating, and comparison with the standard ΛCDM framework. The primary falsifiable prediction of the framework is the Geometry–Growth Projection Test (GGPT), which predicts a systematic decoupling between geometric and growth observables, Δ(fσ₈) ≈ −5% to −7% around z ≈ 1–1.5, potentially testable by Euclid DR1, DESI, and Rubin/LSST. This release contains: 29-page manuscript 28 figures Full observational comparison framework Constraint logic C1–C20 Difference–Gradient–Reconstruction (DGR) methodology Joint parameter constraint framework Cross-scale consistency analysis Falsifiability assessment and GGPT prediction Reproducible demonstration code All figures, numerical examples, likelihoods, and parameter constraints are illustrative and are intended for framework demonstration only. No formal parameter fitting to observational datasets is performed in this work.