Structural Cosmology v3.6: Euclid DR1 Integration and First Nonlinear Constraints An Illustrative Framework for Geometry–Growth Tests, Weak Lensing Assessment, and Multi-Survey Structural Cosmology

Structural Cosmology v3. 6 presents the first integration framework connecting the nonlinear theoretical developments of Structural Cosmology v3. 5 with Euclid DR1 observational analyses. Building upon the nonlinear structure formation framework, higher-order statistics, structural screening, information saturation, relativistic corrections, and baryonic dissipation introduced in v3. 5, this release develops an end-to-end framework for evaluating Structural Cosmology predictions using Euclid DR1 observables. The central illustrative prediction is the Gravitational–Geometric Projection Test (GGPT), which proposes a possible geometry–growth decoupling signature, Δ (fσ₈) ≈ −5% to −7% near redshift z ≈ 1. 0–1. 5. To evaluate this possibility, v3. 6 introduces a complete Euclid DR1 analysis framework including: Galaxy clustering observables (BAO, RSD, fσ₈) Weak lensing and cosmic shear analyses Photometric redshift integration Bayesian posterior-update frameworks Structural Cosmology versus ΛCDM model comparison Structural non-Gaussianity sensitivity forecasts (fNLₛtruct) Expanded falsifiability criteria C1–C66 Updated survival-map methodology A roadmap toward multi-survey structural cosmology (DESI, LSST/Rubin, CMB-S4, SKA, and gravitational-wave standard sirens) The work emphasizes reproducible and falsifiable analysis design while maintaining a reviewer-safe distinction between illustrative framework demonstrations and actual observational results. All measurements, posterior distributions, sensitivity forecasts, and survival-map classifications presented in this release are illustrative framework examples intended to demonstrate analysis methodology. Scientific conclusions require future application to real observational datasets. This release contains 50 figures and accompanying Python demonstration code illustrating the Euclid DR1 integration pipeline, geometry–growth testing strategy, weak-lensing assessment framework, model-comparison methodology, non-Gaussianity sensitivity forecasts, and roadmap development toward future versions of Structural Cosmology.